[firedrake] Concatenation of function spaces?

[Lawrence Mitchell]

> On 24 Jul 2015, at 11:25, Justin Chang <jychang48 at gmail.com> wrote:
> 
> 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:


Aha, this is a simple problem.  When you define a MixedFunctionSpace and then want to apply boundary conditions on a part of the space, you must define the boundary condition on an indexed subspace, rather than the original space.

That is:

V = ...
Q = ...

W = V*Q

bc = DirichletBC(W.sub(1), ...)

rather than

bc = DirichletBC(Q, ...)

This is in the documentation (http://firedrakeproject.org/variational-problems.html#incorporating-boundary-conditions) but maybe not clearly enough.

Making this change, and your code runs fine.

I note in passing, that the DirichletBC constructor can take a list of boundary ids as well as just a single id.  So, since all the boundary condition values are the same you can replace your six separate BC objects by:

bcs = DirichletBC(W.sub(1), 0, (1, 2, 3, 4, 5, 6), method="geometric")

Cheers,

Lawrence
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