[firedrake] Concatenation of function spaces?

[Andrew McRae]

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.


On 22 July 2015 at 05:55, Justin Chang <jychang48 at gmail.com> wrote:

>   Hi everyone,
>
>  Apologies for sending out so many e-mails in such a short amount of time.
> I guess I have a two part question:
>
>  1) Is it possible to concatenation two or more function spaces? In
> FEniCS I was able to do something like this:
>
> V = VectorFunctionSpace(mesh, "CG", 2)
> Q = FunctionSpace(mesh, "CG", 1)
> P = FunctionSpace(mesh, "DG", 0)
> W = V * (Q + P)
>
>  But the above does not work with Firedrake. Is there a way to do that,
> or is there something better? This kind of leads me to the second question:
>
>  2) I would like to try Q2-P1disc elements for Darcy problem (I see that
> this element combination is commonly used for stokes equations, but I don't
> know if it will work for Darcy). Is this possible to do?
>
>  If the answer to the above two is no, is there another "locally
> conservative" mixed formulation that's currently doable other than the
> classical forms like RT0? And preferably with a higher order rate of
> convergence?
>
>  Thanks,
>  Justin
>
>
>
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