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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 | # Copyright (C) 2008 Kristian B. Oelgaard
#
# 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: 2008-03-31
# Last changed: 2008-03-31
#
# The linearised bilinear form a(u,v) and linear form L(v) for
# the nonlinear equation - div (1+u) grad u = f (non-linear Poisson)
element = FiniteElement("Lagrange", triangle, 2)
QE = FiniteElement("Quadrature", triangle, 3)
sig = VectorElement("Quadrature", triangle, 3)
v = TestFunction(element)
u = TrialFunction(element)
u0= Coefficient(element)
C = Coefficient(QE)
sig0 = Coefficient(sig)
f = Coefficient(element)
a = v.dx(i)*C*u.dx(i)*dx + v.dx(i)*2*u0*u*u0.dx(i)*dx
L = v*f*dx - dot(grad(v), sig0)*dx
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