/usr/share/doc/python-ffc/demo/PoissonDG.ufl is in python-ffc 2017.2.0.post0-2.
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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 52 53 54 55 56 57 58 59 | # Copyright (C) 2006-2007 Kristian B. Oelgaard 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: 2006-12-05
# Last changed: 2011-03-08
#
# The bilinear form a(u, v) and linear form L(v) for
# Poisson's equation in a discontinuous Galerkin (DG)
# formulation.
#
# Compile this form with FFC: ffc PoissonDG.ufl
# Elements
element = FiniteElement("Discontinuous Lagrange", triangle, 1)
# Trial and test functions
u = TrialFunction(element)
v = TestFunction(element)
# Facet normal, mesh size and right-hand side
n = FacetNormal(triangle)
h = 2.0*Circumradius(triangle)
f = Coefficient(element)
# Compute average of mesh size
h_avg = (h('+') + h('-'))/2.0
# Neumann boundary conditions
gN = Coefficient(element)
# Parameters
alpha = 4.0
gamma = 8.0
# Bilinear form
a = inner(grad(u), grad(v))*dx \
- inner(jump(u, n), avg(grad(v)))*dS \
- inner(avg(grad(u)), jump(v, n))*dS \
+ alpha/h_avg*inner(jump(u, n), jump(v, n))*dS \
- inner(u*n, grad(v))*ds \
- inner(grad(u), v*n)*ds \
+ gamma/h*u*v*ds
# Linear form
L = f*v*dx + gN*v*ds
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