# Copyright (C) 2004-2007 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
#
# Last changed: 2009-03-02
#
# The bilinear form for the nonlinear term in the
# Navier-Stokes equations with fixed convective velocity.
from ufl_legacy import (Coefficient, TestFunction, TrialFunction, VectorElement, dot,
                        dx, grad, tetrahedron)

cell = tetrahedron
element = VectorElement("Lagrange", cell, 1)

v = TestFunction(element)
u = TrialFunction(element)
w = Coefficient(element)

Du = grad(u)
a = dot(dot(w, Du), v) * dx
