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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) 2006-2007 Kristiand Oelgaard and 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/>.
#
# First added: 2006-12-05
# Last changed: 2007-07-15
#
# The bilinear form a(v, u) and linear form L(v) for
# Poisson's equation in a discontinuous Galerkin (DG)
# formulation.
element = FiniteElement("Discontinuous Lagrange", triangle, 1)
v = TestFunction(element)
u = TrialFunction(element)
f = Coefficient(element)
n = FacetNormal(triangle)
h = Constant(triangle)
gN = Coefficient(element)
alpha = 4.0
gamma = 8.0
a = inner(grad(v), grad(u))*dx \
- inner(avg(grad(v)), jump(u, n))*dS \
- inner(jump(v, n), avg(grad(u)))*dS \
+ alpha/h('+')*dot(jump(v, n), jump(u, n))*dS \
- inner(grad(v), u*n)*ds \
- inner(v*n, grad(u))*ds \
+ gamma/h*v*u*ds
L = v*f*dx + v*gN*ds
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