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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 | # Copyright (C) 2008-2010 Marie Rognes
#
# This file is part of UFL.
#
# UFL 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.
#
# UFL 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 UFL. If not, see <http://www.gnu.org/licenses/>.
#
# First added: 2008-10-03
# Last changed: 2011-07-22
# Define vectorized skew operator
def skw(tau):
sk = 2*skew(tau)
return as_vector((sk[0,1], sk[0,2], sk[1,2]))
cell = tetrahedron
n = 3
# Finite element exterior calculus syntax
r = 1
S = VectorElement("P Lambda", cell, r, form_degree=n-1)
V = VectorElement("P Lambda", cell, r-1, form_degree=n)
Q = VectorElement("P Lambda", cell, r-1, form_degree=n)
# Alternative syntax:
# S = VectorElement("BDM", cell, r)
# V = VectorElement("Discontinuous Lagrange", cell, r-1)
# Q = VectorElement("Discontinuous Lagrange", cell, r-1)
W = MixedElement(S, V, Q)
(sigma, u, gamma) = TrialFunctions(W)
(tau, v, eta) = TestFunctions(W)
a = (inner(sigma, tau) - tr(sigma)*tr(tau)
+ dot(div(tau), u) - dot(div(sigma), v)
+ inner(skw(tau), gamma) + inner(skw(sigma), eta))*dx
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