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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 | # Copyright (C) 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/>.
"""
This demo illustrates the FEEC notation
V = FiniteElement("P Lambda", cell, r, k)
V = FiniteElement("P- Lambda", cell, r, k)
and their aliases.
"""
from ufl import exterior_derivative as d
set_level(INFO)
cells = [interval, triangle, tetrahedron]
r = 1
for cell in cells:
for family in ["P Lambda", "P- Lambda"]:
tdim = cell.topological_dimension()
for k in range(0, tdim+1):
# Testing exterior derivative
V = FiniteElement(family, cell, r, form_degree=k)
v = TestFunction(V)
u = TrialFunction(V)
a = inner(d(u), d(v))*dx
# Testing mixed formulation of Hodge Laplace
if k > 0 and k < tdim+1:
S = FiniteElement(family, cell, r, form_degree=k-1)
W = S * V
(sigma, u) = TrialFunctions(W)
(tau, v) = TestFunctions(W)
a = (inner(sigma, tau) - inner(d(tau), u)
+ inner(d(sigma), v) + inner(d(u), d(v)))*dx
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