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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 | #!/usr/bin/env python
# Copyright (C) 2009 Kristian B. Oelgaard, Garth N. Wells and Anders Logg
#
# This file is part of FFC.
#
# FFC is free software: you can redistribute it and/or modify
# it under the terms of the GNU Lesser General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# FFC is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with FFC. If not, see <http://www.gnu.org/licenses/>.
#
# First added: 2009-06-26
# Last changed: 2011-03-08
#
# The bilinear form a(u, v) and linear form L(v) for
# Biharmonic equation in a discontinuous Galerkin (DG)
# formulation.
#
# Compile this form with FFC: ffc -l dolfin Biharmonic.ufl
# Elements
element = FiniteElement("Lagrange", triangle, 2)
# Trial and test functions
u = TrialFunction(element)
v = TestFunction(element)
f = Coefficient(element)
# Normal component, mesh size and right-hand side
n = element.cell().n
h = Constant(triangle)
# Parameters
alpha = Constant(triangle)
# Bilinear form
a = inner(div(grad(u)), div(grad(v)))*dx \
- inner(jump(grad(u), n), avg(div(grad(v))))*dS \
- inner(avg(div(grad(u))), jump(grad(v), n))*dS \
+ alpha('+')/h('+')*inner(jump(grad(u),n), jump(grad(v),n))*dS
# Linear form
L = f*v*dx
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