# Copyright (C) 2016 Jan Blechta
#
# This file is part of FFCx.
#
# FFCx 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.
#
# FFCx 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 FFCx. If not, see <http://www.gnu.org/licenses/>.
"""Vector constant demo.

The bilinear form a(u, v) and linear form L(v) for
Poisson's equation using bilinear elements on bilinear mesh geometry.
"""

import basix.ufl
from ufl import (
    Coefficient,
    Constant,
    FunctionSpace,
    Mesh,
    TestFunction,
    TrialFunction,
    dx,
    grad,
    inner,
)

coords = basix.ufl.element("P", "triangle", 2, shape=(2,))
mesh = Mesh(coords)
dx = dx(mesh)

element = basix.ufl.element("P", mesh.ufl_cell().cellname, 2)
space = FunctionSpace(mesh, element)

u = TrialFunction(space)
v = TestFunction(space)
f = Coefficient(space)

L = inner(f, v) * dx

mu = Constant(mesh, shape=(3,))
theta = -(mu[1] - 2) / mu[0] - (2 * (2 * mu[0] - 2) * (mu[0] - 1)) / (mu[0] * (mu[1] - 2))
a = theta * inner(grad(u), grad(v)) * dx
