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//----------------------------  hp_fe_values.h  ---------------------------
//    $Id: fe_values.h 20602 2010-02-13 17:44:17Z bangerth $
//    Version: $Name$
//
//    Copyright (C) 2003, 2004, 2006, 2007, 2008, 2009 by the deal.II authors
//
//    This file is subject to QPL and may not be  distributed
//    without copyright and license information. Please refer
//    to the file deal.II/doc/license.html for the  text  and
//    further information on this license.
//
//----------------------------  hp_fe_values.h  ---------------------------
#ifndef __deal2__hp_fe_values_h
#define __deal2__hp_fe_values_h

#include <base/config.h>
#include <fe/fe.h>
#include <hp/fe_collection.h>
#include <hp/q_collection.h>
#include <hp/mapping_collection.h>
#include <fe/fe_values.h>

#include <map>
#include <base/std_cxx1x/shared_ptr.h>

DEAL_II_NAMESPACE_OPEN

template <int dim, int spacedim> class MappingQ1;
template <int dim, int spacedim> class FiniteElement;



namespace internal
{
  namespace hp
  {
/**
 * Base class for the <tt>hp::FE*Values</tt> classes, storing the data
 * that is common to them. The main task of this class is to provide a
 * table where for every combination of finite element, mapping, and
 * quadrature object from their corresponding collection objects there
 * is a matching ::FEValues, ::FEFaceValues, or ::FESubfaceValues
 * object. To make things more efficient, however, these FE*Values
 * objects are only created once requested (lazy allocation).
 *
 * The first template parameter denotes the space dimension we are in,
 * the second the dimensionality of the object that we integrate on,
 * i.e. for usual @p hp::FEValues it is equal to the first one, while
 * for face integration it is one less. The third template parameter
 * indicates the type of underlying non-hp FE*Values base type,
 * i.e. it could either be dealii::FEValues, dealii::FEFaceValues, or
 * dealii::FESubfaceValues.
 * 
 * @ingroup hp
 *
 * @author Wolfgang Bangerth, 2003
 */
    template <int dim, int q_dim, class FEValues>
    class FEValuesBase 
    {
      public:        
                                         /**
                                          * Constructor. Set the fields
                                          * of this class to the values
                                          * indicated by the parameters
                                          * to the constructor.
                                          */
      FEValuesBase (const dealii::hp::MappingCollection<dim,FEValues::space_dimension> &mapping_collection,
		    const dealii::hp::FECollection<dim,FEValues::space_dimension>      &fe_collection,
                      const dealii::hp::QCollection<q_dim>     &q_collection,
                      const UpdateFlags             update_flags);
                                         /**
                                          * Constructor. Set the fields
                                          * of this class to the values
                                          * indicated by the parameters
                                          * to the constructor, and
                                          * choose a @p MappingQ1
                                          * object for the mapping
                                          * object.
                                          */
      FEValuesBase (const dealii::hp::FECollection<dim,FEValues::space_dimension> &fe_collection,
                      const dealii::hp::QCollection<q_dim> &q_collection,
                      const UpdateFlags         update_flags);

					 /**
					  * Get a reference to the
					  * collection of finite
					  * element objects used here.
					  */
	const dealii::hp::FECollection<dim,FEValues::space_dimension> &
	get_fe_collection () const;
	
                                         /**
                                          * Return a reference to the @p
                                          * FEValues object selected by the
                                          * last call to
                                          * select_fe_values(). select_fe_values()
                                          * in turn is called when you called
                                          * the @p reinit function of the
                                          * <tt>hp::FE*Values</tt> class the
                                          * last time.
                                          */
        const FEValues & get_present_fe_values () const;

      protected:

                                         /**
                                          * Select a FEValues object
                                          * suitable for the given FE,
                                          * quadrature, and mapping
                                          * indices. If such an object
                                          * doesn't yet exist, create
                                          * one.
                                          *
                                          * The function returns a
                                          * writable reference so that
                                          * derived classes can also
                                          * reinit() the selected
                                          * FEValues object.
                                          */
        FEValues &
        select_fe_values (const unsigned int fe_index,
                          const unsigned int mapping_index,
                          const unsigned int q_index);

      protected:
                                         /**
                                          * A pointer to the
                                          * collection of finite
                                          * elements to be used.
                                          */
        const SmartPointer<const dealii::hp::FECollection<dim,FEValues::space_dimension>,
			   FEValuesBase<dim,q_dim,FEValues> > fe_collection;
        
                                         /**
                                          * A pointer to the
                                          * collection of mappings to
                                          * be used.
                                          */
        const SmartPointer<const dealii::hp::MappingCollection<dim, FEValues::space_dimension>,
			   FEValuesBase<dim,q_dim,FEValues> > mapping_collection;
    
                                         /**
                                          * Copy of the quadrature
                                          * collection object
                                          * provided to the
                                          * constructor.
                                          */
        const dealii::hp::QCollection<q_dim> q_collection;

      private:
                                         /**
                                          * A table in which we store
                                          * pointers to fe_values
                                          * objects for different
                                          * finite element, mapping,
                                          * and quadrature objects
                                          * from our collection. The
                                          * first index indicates the
                                          * index of the finite
                                          * element within the
                                          * fe_collection, the second
                                          * the index of the mapping
                                          * within the mapping
                                          * collection, and the last
                                          * one the index of the
                                          * quadrature formula within
                                          * the q_collection.
                                          *
                                          * Initially, all entries
                                          * have zero pointers, and we
                                          * will allocate them lazily
                                          * as needed in
                                          * select_fe_values().
                                          */
        Table<3,std_cxx1x::shared_ptr<FEValues> > fe_values_table;

                                         /**
                                          * Set of indices pointing at
                                          * the fe_values object
                                          * selected last time the
                                          * select_fe_value() function
                                          * was called.
                                          */
        TableIndices<3> present_fe_values_index;
        
                                         /**
                                          * Values of the update flags as
                                          * given to the constructor.
                                          */
        const UpdateFlags update_flags;
    };

  }
  
}


namespace hp
{
  
/**
 * An hp equivalent of the ::FEValues class. See the step-27
 * tutorial program for examples of use.
 *
 * The idea of this class is as follows: when one assembled matrices in the hp
 * finite element method, there may be different finite elements on different
 * cells, and consequently one may also want to use different quadrature
 * formulas for different cells. On the other hand, the ::FEValues efficiently
 * handles pre-evaluating whatever information is necessary for a single
 * finite element and quadrature object. This class brings these concepts
 * together: it provides a "collection" of ::FEValues objects.
 *
 * Upon construction, one passes not one finite element and quadrature object
 * (and possible a mapping), but a whole collection of type hp::FECollection
 * and hp::QCollection. Later on, when one sits on a concrete cell, one would
 * call the reinit() function for this particular cell, just as one does for a
 * regular ::FEValues object. The difference is that this time, the reinit()
 * function looks up the active_fe_index of that cell, if necessary creates a
 * ::FEValues object that matches the finite element and quadrature formulas
 * with that particular index in their collections, and then re-initializes it
 * for the current cell. The ::FEValues object that then fits the finite
 * element and quadrature formula for the current cell can then be accessed
 * using the get_present_fe_values() function, and one would work with it just
 * like with any ::FEValues object for non-hp DoF handler objects.
 *
 * The reinit() functions have additional arguments with default values. If
 * not specified, the function takes the index into the hp::FECollection,
 * hp::QCollection, and hp::MappingCollection objects from the active_fe_index
 * of the cell, as explained above. However, one can also select different
 * indices for a current cell. For example, by specifying a different index
 * into the hp::QCollection class, one does not need to sort the quadrature
 * objects in the quadrature collection so that they match one-to-one the
 * order of finite element objects in the FE collection (even though choosing
 * such an order is certainly convenient).
 *
 * Note that ::FEValues objects are created on the fly, i.e. only as they are
 * needed. This ensures that we do not create objects for every combination of
 * finite element, quadrature formula and mapping, but only those that will
 * actually be needed.
 *
 * This class has not yet been implemented for the use in the codimension
 * one case (<tt>spacedim != dim </tt>).
 *
 * @ingroup hp hpcollection
 * @author Wolfgang Bangerth, 2003
 */  
  template <int dim, int spacedim=dim>
    class FEValues : public internal::hp::FEValuesBase<dim,dim,dealii::FEValues<dim,spacedim> >
  {
    public:
 
    static const unsigned int dimension = dim;

    static const unsigned int space_dimension = spacedim;

                                       /**
                                        * Constructor. Initialize this
                                        * object with the given
                                        * parameters.
                                        *
                                        * The finite element
                                        * collection parameter is
                                        * actually ignored, but is in
                                        * the signature of this
                                        * function to make it
                                        * compatible with the
                                        * signature of the respective
                                        * constructor of the usual
                                        * FEValues object, with
                                        * the respective parameter in
                                        * that function also being the
                                        * return value of the
                                        * <tt>DoFHandler::get_fe()</tt>
                                        * function.
                                        */
    FEValues (const dealii::hp::MappingCollection<dim,spacedim> &mapping_collection,
	      const dealii::hp::FECollection<dim,spacedim>  &fe_collection,
                const dealii::hp::QCollection<dim>       &q_collection,
                const UpdateFlags             update_flags);


                                       /**
                                        * Constructor. Initialize this
                                        * object with the given
                                        * parameters, and choose a
                                        * @p MappingQ1 object for the
                                        * mapping object.
                                        *
                                        * The finite element
                                        * collection parameter is
                                        * actually ignored, but is in
                                        * the signature of this
                                        * function to make it
                                        * compatible with the
                                        * signature of the respective
                                        * constructor of the usual
                                        * FEValues object, with
                                        * the respective parameter in
                                        * that function also being the
                                        * return value of the
                                        * <tt>DoFHandler::get_fe()</tt>
                                        * function.
                                        */
    FEValues (const hp::FECollection<dim,spacedim> &fe_collection,
                const hp::QCollection<dim>      &q_collection,
                const UpdateFlags            update_flags);


                                       /**
                                        * Reinitialize the object for
                                        * the given cell.
                                        *
                                        * After the call, you can get
                                        * an FEValues object using the
                                        * get_present_fe_values()
                                        * function that corresponds to
                                        * the present cell. For this
                                        * FEValues object, we use the
                                        * additional arguments
                                        * described below to determine
                                        * which finite element,
                                        * mapping, and quadrature
                                        * formula to use. They are
                                        * order in such a way that the
                                        * arguments one may want to
                                        * change most frequently come
                                        * first. The rules for these
                                        * arguments are as follows:
                                        *
                                        * If the @p fe_index argument
                                        * to this function is left at
                                        * its default value, then we
                                        * use that finite element
                                        * within the hp::FECollection
                                        * passed to the constructor of
                                        * this class with index given
                                        * by
                                        * <code>cell-@>active_fe_index()</code>. Consequently,
                                        * the hp::FECollection
                                        * argument given to this
                                        * object should really be the
                                        * same as that used in the
                                        * construction of the
                                        * hp::DofHandler associated
                                        * with the present cell. On
                                        * the other hand, if a value
                                        * is given for this argument,
                                        * it overrides the choice of
                                        * <code>cell-@>active_fe_index()</code>.
                                        *
                                        * If the @p q_index argument
                                        * is left at its default
                                        * value, then we use that
                                        * quadrature formula within
                                        * the hp::QCollection passed
                                        * to the constructor of this
                                        * class with index given by
                                        * <code>cell-@>active_fe_index()</code>,
                                        * i.e. the same index as that
                                        * of the finite element. In
                                        * this case, there should be a
                                        * corresponding quadrature
                                        * formula for each finite
                                        * element in the
                                        * hp::FECollection. As a
                                        * special case, if the
                                        * quadrature collection
                                        * contains only a single
                                        * element (a frequent case if
                                        * one wants to use the same
                                        * quadrature object for all
                                        * finite elements in an hp
                                        * discretization, even if that
                                        * may not be the most
                                        * efficient), then this single
                                        * quadrature is used unless a
                                        * different value for this
                                        * argument is specified. On
                                        * the other hand, if a value
                                        * is given for this argument,
                                        * it overrides the choice of
                                        * <code>cell-@>active_fe_index()</code>
                                        * or the choice for the single
                                        * quadrature.
                                        *
                                        * If the @p mapping_index
                                        * argument is left at its
                                        * default value, then we use
                                        * that mapping object within
                                        * the hp::MappingCollection
                                        * passed to the constructor of
                                        * this class with index given
                                        * by
                                        * <code>cell-@>active_fe_index()</code>,
                                        * i.e. the same index as that
                                        * of the finite
                                        * element. As above, if the
                                        * mapping collection contains
                                        * only a single element (a
                                        * frequent case if one wants
                                        * to use a MappingQ1 object
                                        * for all finite elements in
                                        * an hp discretization), then
                                        * this single mapping is used
                                        * unless a different value for
                                        * this argument is specified.
                                        */
      void
      reinit (const typename hp::DoFHandler<dim,spacedim>::cell_iterator &cell,
              const unsigned int q_index = numbers::invalid_unsigned_int,
              const unsigned int mapping_index = numbers::invalid_unsigned_int,
              const unsigned int fe_index = numbers::invalid_unsigned_int);

                                       /**
                                        * Like the previous function,
                                        * but for non-hp
                                        * iterators. The reason this
                                        * (and the other non-hp
                                        * iterator) function exists is
                                        * so that one can use
                                        * hp::FEValues not only for
                                        * hp::DoFhandler objects, but
                                        * for all sorts of DoFHandler
                                        * objects, and triangulations
                                        * not associated with
                                        * DoFHandlers in general.
                                        *
                                        * Since
                                        * <code>cell-@>active_fe_index()</code>
                                        * always returns zero for
                                        * non-hp iterators, this
                                        * function chooses the zero-th
                                        * finite element, mapping, and
                                        * quadrature object from the
                                        * relevant constructions
                                        * passed to the constructor of
                                        * this object. The only
                                        * exception is if you specify
                                        * a value different from the
                                        * default value for any of
                                        * these last three arguments.
                                        */
      void
      reinit (const typename dealii::DoFHandler<dim,spacedim>::cell_iterator &cell,
              const unsigned int q_index = numbers::invalid_unsigned_int,
              const unsigned int mapping_index = numbers::invalid_unsigned_int,
              const unsigned int fe_index = numbers::invalid_unsigned_int);

                                       /**
                                        * Like the previous function,
                                        * but for non-hp
                                        * iterators. The reason this
                                        * (and the other non-hp
                                        * iterator) function exists is
                                        * so that one can use
                                        * hp::FEValues not only for
                                        * hp::DoFhandler objects, but
                                        * for all sorts of DoFHandler
                                        * objects, and triangulations
                                        * not associated with
                                        * DoFHandlers in general.
                                        *
                                        * Since
                                        * <code>cell-@>active_fe_index()</code>
                                        * always returns zero for
                                        * non-hp iterators, this
                                        * function chooses the zero-th
                                        * finite element, mapping, and
                                        * quadrature object from the
                                        * relevant constructions
                                        * passed to the constructor of
                                        * this object. The only
                                        * exception is if you specify
                                        * a value different from the
                                        * default value for any of
                                        * these last three arguments.
                                        */
      void
      reinit (const typename MGDoFHandler<dim,spacedim>::cell_iterator &cell,
              const unsigned int q_index = numbers::invalid_unsigned_int,
              const unsigned int mapping_index = numbers::invalid_unsigned_int,
              const unsigned int fe_index = numbers::invalid_unsigned_int);
      
                                       /**
                                        * Like the previous function,
                                        * but for non-hp
                                        * iterators. The reason this
                                        * (and the other non-hp
                                        * iterator) function exists is
                                        * so that one can use
                                        * hp::FEValues not only for
                                        * hp::DoFhandler objects, but
                                        * for all sorts of DoFHandler
                                        * objects, and triangulations
                                        * not associated with
                                        * DoFHandlers in general.
                                        *
                                        * Since
                                        * <code>cell-@>active_fe_index()</code>
                                        * doesn't make sense for
                                        * triangulation iterators,
                                        * this function chooses the
                                        * zero-th finite element,
                                        * mapping, and quadrature
                                        * object from the relevant
                                        * constructions passed to the
                                        * constructor of this
                                        * object. The only exception
                                        * is if you specify a value
                                        * different from the default
                                        * value for any of these last
                                        * three arguments.
                                        */
      void
      reinit (const typename Triangulation<dim,spacedim>::cell_iterator &cell,
              const unsigned int q_index = numbers::invalid_unsigned_int,
              const unsigned int mapping_index = numbers::invalid_unsigned_int,
              const unsigned int fe_index = numbers::invalid_unsigned_int);


  };



/**
 * This is the equivalent of the hp::FEValues class but for face integrations,
 * i.e. it is to hp::FEValues what ::FEFaceValues is to ::FEValues.
 *
 * The same comments apply as in the documentation of the hp::FEValues
 * class. However, it is important to note that it is here more common that
 * one would want to explicitly specify an index to a particular quadrature
 * formula in the reinit() functions. This is because the default index
 * corresponds to the finite element index on the current function. On the
 * other hand, integration on faces will typically have to happen with a
 * quadrature formula that is adjusted to the finite elements used on both
 * sides of a face. If one sorts the elements of the hp::FECollection with
 * ascending polynomial degree, and matches these finite elements with
 * corresponding quadrature formulas in the hp::QCollection passed to the
 * constructor, then the quadrature index passed to the reinit() function
 * should typically be something like <code>std::max
 * (cell-@>active_fe_index(), neighbor-@>active_fe_index()</code> to ensure
 * that a quadrature formula is chosen that is sufficiently accurate for
 * <em>both</em> finite elements.
 *
 * @ingroup hp hpcollection
 * @author Wolfgang Bangerth, 2003
 */  
  template <int dim>
  class FEFaceValues : public internal::hp::FEValuesBase<dim,dim-1,dealii::FEFaceValues<dim> >
  {
    public:
                                       /**
                                        * Constructor. Initialize this
                                        * object with the given
                                        * parameters.
                                        *
                                        * The finite element
                                        * collection parameter is
                                        * actually ignored, but is in
                                        * the signature of this
                                        * function to make it
                                        * compatible with the
                                        * signature of the respective
                                        * constructor of the usual
                                        * FEValues object, with
                                        * the respective parameter in
                                        * that function also being the
                                        * return value of the
                                        * <tt>DoFHandler::get_fe()</tt>
                                        * function.
                                        */
      FEFaceValues (const hp::MappingCollection<dim> &mapping_collection,
                    const hp::FECollection<dim>  &fe_collection,
                    const hp::QCollection<dim-1>     &q_collection,
                    const UpdateFlags             update_flags);


                                       /**
                                        * Constructor. Initialize this
                                        * object with the given
                                        * parameters, and choose a
                                        * @p MappingQ1 object for the
                                        * mapping object.
                                        *
                                        * The finite element
                                        * collection parameter is
                                        * actually ignored, but is in
                                        * the signature of this
                                        * function to make it
                                        * compatible with the
                                        * signature of the respective
                                        * constructor of the usual
                                        * FEValues object, with
                                        * the respective parameter in
                                        * that function also being the
                                        * return value of the
                                        * <tt>DoFHandler::get_fe()</tt>
                                        * function.
                                        */
      FEFaceValues (const hp::FECollection<dim>  &fe_collection,
                    const hp::QCollection<dim-1> &q_collection,
                    const UpdateFlags             update_flags);

                                       /**
                                        * Reinitialize the object for
                                        * the given cell and face.
                                        *
                                        * After the call, you can get
                                        * an FEFaceValues object using the
                                        * get_present_fe_values()
                                        * function that corresponds to
                                        * the present cell. For this
                                        * FEFaceValues object, we use the
                                        * additional arguments
                                        * described below to determine
                                        * which finite element,
                                        * mapping, and quadrature
                                        * formula to use. They are
                                        * order in such a way that the
                                        * arguments one may want to
                                        * change most frequently come
                                        * first. The rules for these
                                        * arguments are as follows:
                                        *
                                        * If the @p fe_index argument
                                        * to this function is left at
                                        * its default value, then we
                                        * use that finite element
                                        * within the hp::FECollection
                                        * passed to the constructor of
                                        * this class with index given
                                        * by
                                        * <code>cell-@>active_fe_index()</code>. Consequently,
                                        * the hp::FECollection
                                        * argument given to this
                                        * object should really be the
                                        * same as that used in the
                                        * construction of the
                                        * hp::DofHandler associated
                                        * with the present cell. On
                                        * the other hand, if a value
                                        * is given for this argument,
                                        * it overrides the choice of
                                        * <code>cell-@>active_fe_index()</code>.
                                        *
                                        * If the @p q_index argument
                                        * is left at its default
                                        * value, then we use that
                                        * quadrature formula within
                                        * the hp::QCollection passed
                                        * to the constructor of this
                                        * class with index given by
                                        * <code>cell-@>active_fe_index()</code>,
                                        * i.e. the same index as that
                                        * of the finite element. In
                                        * this case, there should be a
                                        * corresponding quadrature
                                        * formula for each finite
                                        * element in the
                                        * hp::FECollection. As a
                                        * special case, if the
                                        * quadrature collection
                                        * contains only a single
                                        * element (a frequent case if
                                        * one wants to use the same
                                        * quadrature object for all
                                        * finite elements in an hp
                                        * discretization, even if that
                                        * may not be the most
                                        * efficient), then this single
                                        * quadrature is used unless a
                                        * different value for this
                                        * argument is specified. On
                                        * the other hand, if a value
                                        * is given for this argument,
                                        * it overrides the choice of
                                        * <code>cell-@>active_fe_index()</code>
                                        * or the choice for the single
                                        * quadrature.
                                        *
                                        * If the @p mapping_index
                                        * argument is left at its
                                        * default value, then we use
                                        * that mapping object within
                                        * the hp::MappingCollection
                                        * passed to the constructor of
                                        * this class with index given
                                        * by
                                        * <code>cell-@>active_fe_index()</code>,
                                        * i.e. the same index as that
                                        * of the finite
                                        * element. As above, if the
                                        * mapping collection contains
                                        * only a single element (a
                                        * frequent case if one wants
                                        * to use a MappingQ1 object
                                        * for all finite elements in
                                        * an hp discretization), then
                                        * this single mapping is used
                                        * unless a different value for
                                        * this argument is specified.
                                        */
      void
      reinit (const typename hp::DoFHandler<dim>::cell_iterator &cell,
              const unsigned int face_no,
              const unsigned int q_index = numbers::invalid_unsigned_int,
              const unsigned int mapping_index = numbers::invalid_unsigned_int,
              const unsigned int fe_index = numbers::invalid_unsigned_int);

                                       /**
                                        * Like the previous function,
                                        * but for non-hp
                                        * iterators. The reason this
                                        * (and the other non-hp
                                        * iterator) function exists is
                                        * so that one can use
                                        * hp::FEValues not only for
                                        * hp::DoFhandler objects, but
                                        * for all sorts of DoFHandler
                                        * objects, and triangulations
                                        * not associated with
                                        * DoFHandlers in general.
                                        *
                                        * Since
                                        * <code>cell-@>active_fe_index()</code>
                                        * always returns zero for
                                        * non-hp iterators, this
                                        * function chooses the zero-th
                                        * finite element, mapping, and
                                        * quadrature object from the
                                        * relevant constructions
                                        * passed to the constructor of
                                        * this object. The only
                                        * exception is if you specify
                                        * a value different from the
                                        * default value for any of
                                        * these last three arguments.
                                        */
      void
      reinit (const typename dealii::DoFHandler<dim>::cell_iterator &cell,
              const unsigned int face_no,
              const unsigned int q_index = numbers::invalid_unsigned_int,
              const unsigned int mapping_index = numbers::invalid_unsigned_int,
              const unsigned int fe_index = numbers::invalid_unsigned_int);

                                       /**
                                        * Like the previous function,
                                        * but for non-hp
                                        * iterators. The reason this
                                        * (and the other non-hp
                                        * iterator) function exists is
                                        * so that one can use
                                        * hp::FEValues not only for
                                        * hp::DoFhandler objects, but
                                        * for all sorts of DoFHandler
                                        * objects, and triangulations
                                        * not associated with
                                        * DoFHandlers in general.
                                        *
                                        * Since
                                        * <code>cell-@>active_fe_index()</code>
                                        * always returns zero for
                                        * non-hp iterators, this
                                        * function chooses the zero-th
                                        * finite element, mapping, and
                                        * quadrature object from the
                                        * relevant constructions
                                        * passed to the constructor of
                                        * this object. The only
                                        * exception is if you specify
                                        * a value different from the
                                        * default value for any of
                                        * these last three arguments.
                                        */
      void
      reinit (const typename MGDoFHandler<dim>::cell_iterator &cell,
              const unsigned int face_no,
              const unsigned int q_index = numbers::invalid_unsigned_int,
              const unsigned int mapping_index = numbers::invalid_unsigned_int,
              const unsigned int fe_index = numbers::invalid_unsigned_int);
      
                                       /**
                                        * Like the previous function,
                                        * but for non-hp
                                        * iterators. The reason this
                                        * (and the other non-hp
                                        * iterator) function exists is
                                        * so that one can use
                                        * hp::FEValues not only for
                                        * hp::DoFhandler objects, but
                                        * for all sorts of DoFHandler
                                        * objects, and triangulations
                                        * not associated with
                                        * DoFHandlers in general.
                                        *
                                        * Since
                                        * <code>cell-@>active_fe_index()</code>
                                        * doesn't make sense for
                                        * triangulation iterators,
                                        * this function chooses the
                                        * zero-th finite element,
                                        * mapping, and quadrature
                                        * object from the relevant
                                        * constructions passed to the
                                        * constructor of this
                                        * object. The only exception
                                        * is if you specify a value
                                        * different from the default
                                        * value for any of these last
                                        * three arguments.
                                        */
      void
      reinit (const typename Triangulation<dim>::cell_iterator &cell,
              const unsigned int face_no,
              const unsigned int q_index = numbers::invalid_unsigned_int,
              const unsigned int mapping_index = numbers::invalid_unsigned_int,
              const unsigned int fe_index = numbers::invalid_unsigned_int);
  };



/**
 * This class implements for subfaces what hp::FEFaceValues does for
 * faces. See there for further documentation.
 *
 * @ingroup hp hpcollection
 * @author Wolfgang Bangerth, 2003
 */  
  template <int dim>
  class FESubfaceValues : public internal::hp::FEValuesBase<dim,dim-1,dealii::FESubfaceValues<dim> >
  {
    public:
                                       /**
                                        * Constructor. Initialize this
                                        * object with the given
                                        * parameters.
                                        *
                                        * The finite element
                                        * collection parameter is
                                        * actually ignored, but is in
                                        * the signature of this
                                        * function to make it
                                        * compatible with the
                                        * signature of the respective
                                        * constructor of the usual
                                        * FEValues object, with
                                        * the respective parameter in
                                        * that function also being the
                                        * return value of the
                                        * <tt>DoFHandler::get_fe()</tt>
                                        * function.
                                        */
      FESubfaceValues (const hp::MappingCollection<dim> &mapping_collection,
                       const hp::FECollection<dim>  &fe_collection,
                       const hp::QCollection<dim-1>     &q_collection,
                       const UpdateFlags             update_flags);


                                       /**
                                        * Constructor. Initialize this
                                        * object with the given
                                        * parameters, and choose a
                                        * @p MappingQ1 object for the
                                        * mapping object.
                                        *
                                        * The finite element
                                        * collection parameter is
                                        * actually ignored, but is in
                                        * the signature of this
                                        * function to make it
                                        * compatible with the
                                        * signature of the respective
                                        * constructor of the usual
                                        * FEValues object, with
                                        * the respective parameter in
                                        * that function also being the
                                        * return value of the
                                        * <tt>DoFHandler::get_fe()</tt>
                                        * function.
                                        */
      FESubfaceValues (const hp::FECollection<dim> &fe_collection,
                       const hp::QCollection<dim-1>    &q_collection,
                       const UpdateFlags            update_flags);

                                       /**
                                        * Reinitialize the object for
                                        * the given cell, face, and subface.
                                        *
                                        * After the call, you can get
                                        * an FESubfaceValues object using the
                                        * get_present_fe_values()
                                        * function that corresponds to
                                        * the present cell. For this
                                        * FESubfaceValues object, we use the
                                        * additional arguments
                                        * described below to determine
                                        * which finite element,
                                        * mapping, and quadrature
                                        * formula to use. They are
                                        * order in such a way that the
                                        * arguments one may want to
                                        * change most frequently come
                                        * first. The rules for these
                                        * arguments are as follows:
                                        *
                                        * If the @p q_index argument
                                        * is left at its default
                                        * value, then we use that
                                        * quadrature formula within
                                        * the hp::QCollection passed
                                        * to the constructor of this
                                        * class with index given by
                                        * <code>cell-@>active_fe_index()</code>,
                                        * i.e. the same index as that
                                        * of the finite element. In
                                        * this case, there should be a
                                        * corresponding quadrature
                                        * formula for each finite
                                        * element in the
                                        * hp::FECollection. As a
                                        * special case, if the
                                        * quadrature collection
                                        * contains only a single
                                        * element (a frequent case if
                                        * one wants to use the same
                                        * quadrature object for all
                                        * finite elements in an hp
                                        * discretization, even if that
                                        * may not be the most
                                        * efficient), then this single
                                        * quadrature is used unless a
                                        * different value for this
                                        * argument is specified. On
                                        * the other hand, if a value
                                        * is given for this argument,
                                        * it overrides the choice of
                                        * <code>cell-@>active_fe_index()</code>
                                        * or the choice for the single
                                        * quadrature.
                                        *
                                        * If the @p mapping_index
                                        * argument is left at its
                                        * default value, then we use
                                        * that mapping object within
                                        * the hp::MappingCollection
                                        * passed to the constructor of
                                        * this class with index given
                                        * by
                                        * <code>cell-@>active_fe_index()</code>,
                                        * i.e. the same index as that
                                        * of the finite
                                        * element. As above, if the
                                        * mapping collection contains
                                        * only a single element (a
                                        * frequent case if one wants
                                        * to use a MappingQ1 object
                                        * for all finite elements in
                                        * an hp discretization), then
                                        * this single mapping is used
                                        * unless a different value for
                                        * this argument is specified.
                                        */
      void
      reinit (const typename hp::DoFHandler<dim>::cell_iterator &cell,
              const unsigned int face_no,
              const unsigned int subface_no,
              const unsigned int q_index = numbers::invalid_unsigned_int,
              const unsigned int mapping_index = numbers::invalid_unsigned_int,
              const unsigned int fe_index = numbers::invalid_unsigned_int);

                                       /**
                                        * Like the previous function,
                                        * but for non-hp
                                        * iterators. The reason this
                                        * (and the other non-hp
                                        * iterator) function exists is
                                        * so that one can use
                                        * hp::FEValues not only for
                                        * hp::DoFhandler objects, but
                                        * for all sorts of DoFHandler
                                        * objects, and triangulations
                                        * not associated with
                                        * DoFHandlers in general.
                                        *
                                        * Since
                                        * <code>cell-@>active_fe_index()</code>
                                        * always returns zero for
                                        * non-hp iterators, this
                                        * function chooses the zero-th
                                        * finite element, mapping, and
                                        * quadrature object from the
                                        * relevant constructions
                                        * passed to the constructor of
                                        * this object. The only
                                        * exception is if you specify
                                        * a value different from the
                                        * default value for any of
                                        * these last three arguments.
                                        */
      void
      reinit (const typename dealii::DoFHandler<dim>::cell_iterator &cell,
              const unsigned int face_no,
              const unsigned int subface_no,
              const unsigned int q_index = numbers::invalid_unsigned_int,
              const unsigned int mapping_index = numbers::invalid_unsigned_int,
              const unsigned int fe_index = numbers::invalid_unsigned_int);

                                       /**
                                        * Like the previous function,
                                        * but for non-hp
                                        * iterators. The reason this
                                        * (and the other non-hp
                                        * iterator) function exists is
                                        * so that one can use
                                        * hp::FEValues not only for
                                        * hp::DoFhandler objects, but
                                        * for all sorts of DoFHandler
                                        * objects, and triangulations
                                        * not associated with
                                        * DoFHandlers in general.
                                        *
                                        * Since
                                        * <code>cell-@>active_fe_index()</code>
                                        * always returns zero for
                                        * non-hp iterators, this
                                        * function chooses the zero-th
                                        * finite element, mapping, and
                                        * quadrature object from the
                                        * relevant constructions
                                        * passed to the constructor of
                                        * this object. The only
                                        * exception is if you specify
                                        * a value different from the
                                        * default value for any of
                                        * these last three arguments.
                                        */
      void
      reinit (const typename MGDoFHandler<dim>::cell_iterator &cell,
              const unsigned int face_no,
              const unsigned int subface_no,
              const unsigned int q_index = numbers::invalid_unsigned_int,
              const unsigned int mapping_index = numbers::invalid_unsigned_int,
              const unsigned int fe_index = numbers::invalid_unsigned_int);
      
                                       /**
                                        * Like the previous function,
                                        * but for non-hp
                                        * iterators. The reason this
                                        * (and the other non-hp
                                        * iterator) function exists is
                                        * so that one can use
                                        * hp::FEValues not only for
                                        * hp::DoFhandler objects, but
                                        * for all sorts of DoFHandler
                                        * objects, and triangulations
                                        * not associated with
                                        * DoFHandlers in general.
                                        *
                                        * Since
                                        * <code>cell-@>active_fe_index()</code>
                                        * doesn't make sense for
                                        * triangulation iterators,
                                        * this function chooses the
                                        * zero-th finite element,
                                        * mapping, and quadrature
                                        * object from the relevant
                                        * constructions passed to the
                                        * constructor of this
                                        * object. The only exception
                                        * is if you specify a value
                                        * different from the default
                                        * value for any of these last
                                        * three arguments.
                                        */
      void
      reinit (const typename Triangulation<dim>::cell_iterator &cell,
              const unsigned int face_no,
              const unsigned int subface_no,
              const unsigned int q_index = numbers::invalid_unsigned_int,
              const unsigned int mapping_index = numbers::invalid_unsigned_int,
              const unsigned int fe_index = numbers::invalid_unsigned_int);
  };
  
}


// -------------- inline and template functions --------------

namespace internal 
{
  namespace hp
  {
    template <int dim, int q_dim, class FEValues>
    inline
    const FEValues &
    FEValuesBase<dim,q_dim,FEValues>::get_present_fe_values () const
    {
      return *fe_values_table(present_fe_values_index);
    }



    template <int dim, int q_dim, class FEValues>
    inline
    const dealii::hp::FECollection<dim,FEValues::space_dimension> &
    FEValuesBase<dim,q_dim,FEValues>::get_fe_collection () const
    {
      return *fe_collection;
    }
  }
  
}

DEAL_II_NAMESPACE_CLOSE

#endif