# Copyright (C) 2009-2010 Anders Logg
#
# 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/>.
"""Facet integrals demo.

Simple example of a form defined over exterior and interior facets.
"""

import basix.ufl
from ufl import (
    FacetNormal,
    FunctionSpace,
    Mesh,
    TestFunction,
    TrialFunction,
    avg,
    dS,
    ds,
    grad,
    inner,
    jump,
)

element = basix.ufl.element("Discontinuous Lagrange", "triangle", 1)
domain = Mesh(basix.ufl.element("Lagrange", "triangle", 1, shape=(2,)))
space = FunctionSpace(domain, element)

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

n = FacetNormal(domain)

a = (
    inner(u, v) * ds
    + inner(u("+"), v("-")) * dS
    + inner(jump(u, n), avg(grad(v))) * dS
    + inner(avg(grad(u)), jump(v, n)) * dS
)