/usr/share/doc/python-ffc/demo/BiharmonicRegge.ufl is in python-ffc 2016.2.0-1.
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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 | # Copyright (C) 2016 Lizao Li
#
# 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/>.
#
# The bilinear form a(u, v) and linear form L(v) for
# Biharmonic equation in Regge formulation.
#
# Compile this form with FFC: ffc -l dolfin BiharmonicRegge.ufl
REG = FiniteElement('Regge', tetrahedron, 1)
CG = FiniteElement('Lagrange', tetrahedron, 2)
mixed_element = REG * CG
(sigma, u) = TrialFunctions(mixed_element)
(tau, v) = TestFunctions(mixed_element)
f = Coefficient(CG)
def S(mu):
return mu - Identity(3) * tr(mu)
def b(mu, v):
n = FacetNormal(tetrahedron)
return inner(S(mu), grad(grad(v))) * dx \
- dot(dot(S(mu('+')), n('+')), n('+')) * jump(grad(v), n) * dS \
- dot(dot(S(mu), n), n) * dot(grad(v), n) * ds
a = inner(S(sigma), S(tau)) * dx - b(tau, u) + b(sigma, v)
L = f * v * dx
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