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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 | # Copyright (C) 2005-2009 Anders Logg
#
# 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/>.
#
# Modified by Martin Sandve Alnes, 2009
#
# The bilinear form a(v, u1) and linear form L(v) for
# one backward Euler step with the heat equation.
#
cell = triangle
element = FiniteElement("Lagrange", cell, 1)
v = TestFunction(element) # Test function
u1 = TrialFunction(element) # Value at t_n
u0 = Coefficient(element) # Value at t_n-1
c = Coefficient(element) # Heat conductivity
f = Coefficient(element) # Heat source
k = Constant(cell) # Time step
a = v*u1*dx + k*c*dot(grad(v), grad(u1))*dx
L = v*u0*dx + k*v*f*dx
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