[firedrake] Concatenation of function spaces?

[Justin Chang]

Thanks for the responses guys. However, I am running into issues regarding
Dirichlet bcs for P2/P0 elements. Attached is the code:

I am trying to apply homogeneous boundary conditions in the P0 space, and
when I looked at the documentation online it said to use DirichletBC(Q,
<value>, <boundary_id>, method="geometric")
 but I am getting these kinds of errors:

Traceback (most recent call last):
  File "Compare_P2P0.py", line 69, in <module>
    solver.solve()
  File "<string>", line 2, in solve
  File "/home/justin/Software/firedrake-deps/PyOP2/pyop2/profiling.py",
line 203, in wrapper
    return f(*args, **kwargs)
  File
"/home/justin/Software/firedrake-deps/firedrake/firedrake/variational_solver.py",
line 165, in solve
    bc.apply(self._problem.u)
  File "<string>", line 2, in apply
  File "/home/justin/Software/firedrake-deps/PyOP2/pyop2/profiling.py",
line 203, in wrapper
    return f(*args, **kwargs)
  File "/home/justin/Software/firedrake-deps/firedrake/firedrake/bcs.py",
line 199, in apply
    raise RuntimeError("%r defined on incompatible FunctionSpace!" % r)
RuntimeError: Coefficient(MixedElement(*[VectorElement('Lagrange',
Domain(Coefficient(VectorElement('Lagrange', Domain(Cell('tetrahedron', 3),
label=None, data='<data with id 140677727926224>'), 1, dim=3,
quad_scheme=None), 1)), 2, dim=3, quad_scheme=None),
FiniteElement('Discontinuous Lagrange',
Domain(Coefficient(VectorElement('Lagrange', Domain(Cell('tetrahedron', 3),
label=None, data='<data with id 140677727926224>'), 1, dim=3,
quad_scheme=None), 1)), 0, quad_scheme=None)], **{'value_shape': (4,) }),
7) defined on incompatible FunctionSpace!


Anyone know what's wrong? Thanks

Thanks

On Wed, Jul 22, 2015 at 3:43 AM, Lawrence Mitchell <
lawrence.mitchell at imperial.ac.uk> wrote:

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> On 22/07/15 07:31, Andrew McRae wrote:
> > 1)  Yes, this can be done in Firedrake.  However, we consider the
> > local element to be enriched, not the function space:
> >
> > V1 = VectorFunctionSpace... Q_elt = FiniteElement("CG", interval,
> > 1) P_elt = FiniteElement("DG", interval, 0) elt = Q_elt + P_elt V2
> > = FunctionSpace(mesh, elt) W = V1 * V2
> >
> > 2)  Is P1disc the same as P1DG?  "All polynomials of degree 1 with
> > no continuity between cells"?  If so, none of us have implemented
> > the P1disc elements on quadrilaterals yet in FIAT.  We have full
> > support for the third column of http://femtable.org/, which has all
> > the "tensor product construction" elements, but not the fourth.  If
> > you want to try implementing P1disc yourself, we can hopefully
> > provide support.
>
> Indeed yes.
>
> Note that P1disc provides some problems for the standard approach of
> pulling back to a reference element and integrating.  Unless your mesh
> is asymptotically affine you only get 1st order convergence in the L_2
> norm of P.  This is because the mapped global space doesn't contain P_k.
>
> See:
>
> Matthies and Tobiska. The Inf-Sup Condition for the Mapped
> $Q_k-P_{k-1}^{\mathrm{disc}}$ Element in Arbitrary Space Dimensions (2002)
>
> and
>
> Boffi and Gastaldi. On the quadrilateral $Q_2–P_1$ element for the
> Stokes problem (2002)
>
> For details.
>
> Lawrence
>
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