# Copyright (C) 2010 Anders Logg
#
# This file is part of DOLFIN.
#
# DOLFIN 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.
#
# DOLFIN 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 DOLFIN. If not, see <http://www.gnu.org/licenses/>.
#
# First added:  2010-08-30
# Last changed: 2011-06-30
#
# The bilinear form a(u, v) and linear form L(v) for the tentative
# velocity step in Chorin's method for the incompressible
# Navier-Stokes equations.
#
# Compile this form with FFC: ffc -l dolfin TentativeVelocity.ufl.

# Define function spaces (P2-P1)
V = VectorElement("CG", triangle, 2)
Q = FiniteElement("CG", triangle, 1)

# Define trial and test functions
u = TrialFunction(V)
v = TestFunction(V)

# Define coefficients
k  = Constant(triangle)
u0 = Coefficient(V)
f  = Coefficient(V)
nu = 0.01

# Define bilinear and linear forms
eq = (1/k)*inner(u - u0, v)*dx + inner(grad(u0)*u0, v)*dx + \
    nu*inner(grad(u), grad(v))*dx - inner(f, v)*dx
a  = lhs(eq)
L  = rhs(eq)