Dear Anna,
On 06/09/16 17:19, Anna Kalogirou wrote:
> Dear all,
>
> I have the following sample code which gives a ValueError: Mismatching
> function spaces.
>
> ##
>
> V = FunctionSpace(mesh, "CG", 1)
> W = V*V
>
> w = Function(W)
> v1, v2 = TestFunctions(W)
> u1, u2 = split(w)
>
> F1 = F(u1, u2) # function of u1 and u2
>
> F2 = F(u2) # function of u2 only
>
> bc = DirichletBC(W.sub(1), u1, 'top’) # BC for F2
>
> u_problem = NonlinearVariationalProblem(F1 + F2, w, bcs=[bc])
>
> ##
>
> Note that the second equation depends on u1 through the DirichletBC
> only. Is the error generated due to the fact that u1 comes from
> W.sub(0) and it is given as a BC on W.sub(0)?
There are two problems here.
1. u1 is indexed with component 0, but you're trying to apply it to
component 1 (which is why you get the proximate error).
2. This is the bigger problem.
The way you've formulated the problem, even if you removed the error
from (1), which would be possible I think, doesn't do what you think
it does. We don't support problems where the solution is coupled to
itself through the boundary condition. So what would happen is you
would end up minimising the residual for F2 subject to the value of u1
on the boundary, *when you started the solve* (i.e. whatever initial
guess you had for u1).
I think it might be possible to vary how firedrake works to do what
you want, but one would have to work out what's going on on paper
first. http://firedrakeproject.org/boundary_conditions.html describes
the maths (and the implementation strategy) for applying boundary
conditions. Can you see how to modify it so that it still works if
the boundary condition value depends on the state variable?
Lawrence