def MaxFacetEdgeLength(mesh: cpp.mesh.Mesh) -> ufl.MaxFacetEdgeLength:
"""Return symbolic maximum facet edge length of a cell
for given mesh.
*Example of usage*
.. code-block:: python
mesh = UnitSquare(4,4)
maxfe = MaxFacetEdgeLength(mesh)
"""
return ufl.MaxFacetEdgeLength(mesh.ufl_domain())
def MaxFacetEdgeLength(mesh):
"""
Return symbolic maximum facet edge length of a cell for given mesh.
*Arguments*
mesh
a :py:class:`Mesh <dolfin.cpp.Mesh>`.
*Example of usage*
.. code-block:: python
mesh = UnitSquare(4,4)
vol = MaxFacetEdgeLength(mesh)
"""
return ufl.MaxFacetEdgeLength(_mesh2domain(mesh))
top = 1.0
if dim == 3:
top = ufl.conditional(x[2] > 1.25, 1, 0)
initial_u = iu(x[1]) * top + iu(2.5 - x[1]) * (1.0 - top)
initial_v = ufl.conditional(x[0] < 1.25, 0.5, 0)
uh = space.interpolate(initial_u, name="u")
uh_n = uh.copy()
vh = space.interpolate(initial_v, name="v")
vh_n = vh.copy()
u = ufl.TrialFunction(space)
phi = ufl.TestFunction(space)
hT = ufl.MaxCellEdgeLength(space.cell())
hS = ufl.avg(ufl.MaxFacetEdgeLength(space.cell()))
hs = ufl.MaxFacetEdgeLength(space.cell())('+')
n = ufl.FacetNormal(space.cell())
ustar = lambda v: (v + spiral_b) / spiral_a
diffusiveFlux = lambda w, d: spiral_D * d
source = lambda u1, u2, u3, v: -1 / spiral_eps * u1 * (1 - u2) * (u3 - ustar(v)
)
source = lambda u1, u2, u3, v: -1 / spiral_eps * u1 * (1 - u2) * (u3 - ustar(v)
)
xForm = inner(diffusiveFlux(u, grad(u)), grad(phi)) * dx
xForm += ufl.conditional(uh_n < ustar(vh_n), source(u, uh_n, uh_n, vh_n),
source(uh_n, u, uh_n, vh_n)) * phi * dx
# <markdowncell>
"newton.verbose": False,
"newton.linear.verbose": False}
scheme = dune.fem.scheme.galerkin(equation,
solver="cg",
parameters=solverParameters)
# <markdowncell>
# Error estimator
# <codecell>
fvspace = dune.fem.space.finiteVolume(uh.space.grid)
estimate = fvspace.interpolate([0], name="estimate")
chi = ufl.TestFunction(fvspace)
hT = ufl.MaxCellEdgeLength(fvspace.cell())
he = ufl.MaxFacetEdgeLength(fvspace.cell())('+')
n = ufl.FacetNormal(fvspace.cell())
residual = (u - uh_n) / dt - div(diffusiveFlux) + source(u, u, u, vh)
estimator_ufl = hT**2 * residual**2 * chi * dx +\
he * inner( jump(diffusiveFlux), n('+'))**2 * avg(chi) * dS
estimator = dune.fem.operator.galerkin(estimator_ufl)
# <markdowncell>
# Time loop
# <codecell>
nextSaveTime = saveInterval
count = 0
levelFunction = dune.fem.function.levelFunction(gridView)