Putting a Dirichlet condition on only one element of a vector function

Hi Garth,

Thanks for the suggestion. I've taken a look at the demo, but it's unclear to me how I can use this.

In the stokes-taylor-hood demo, a MixedFunctionSpace is defined, consisting of a VectorFunctionSpace and a FunctionSpace. Dirichlet conditions are then imposed on each of the subspaces using W.sub(i). This I understand.

However, within the VectorFunctionSpace V, dirichlet conditions are imposed on each component of the vector on each Dirichlet boundary, e.g. the lines:

inflow = Expression(("-sin(x[1]*pi)", "0.0", "0.0"))
bc1 = DirichletBC(W.sub(0), inflow, right)

impose Dirichlet conditions on u[0], u[1] and u[2].

By contrast, I wish to impose conditions on one component only. For example, one condition might be "restrict solutions to those vectors whose second component is zero on the boundary, but allow the other two components to be determined by a boundary integral".

One thing that I had thought of was to create a nested function space, with a vector space defined as:

Q = FunctionSpace(mesh, "CG", 2)
V = MixedFunctionSpace([Q,Q,Q])

Then impose Dirichlet conditions on only (say) the second element of the solution using V.sub(1).

Is this a reasonable approach?

For clarity, by "nested function space", I was referring to the fact that, on top of this space V, I would require an extra space for a lagrange multiplier, e.g.

Q = FunctionSpace(mesh, "CG", 2)
V = MixedFunctionSpace([Q,Q,Q])
R = FunctionSpace(mesh, "R", 0)
W = V*R

Where R is the space containing the lagrange multiplier.

Sorry if that caused confusion, it's not terribly relevant to the problem at hand.

Sorry, I think I've just discovered what you meant.

From the FEniCS documentation on the SubSpace class:

"A typical example is the function space W = V x P for Stokes. Here, V = W[0] is the subspace for the velocity component and P = W[1] is the subspace for the pressure component. Furthermore, W[0][0] = V[0] is the first component of the velocity space etc."

I assume what you mean is that I can apply DirichletBC to V[1] only. I will test this and see how I get on.

Sorry for not looking harder before posting replies!

Thanks Garth Wells, that solved my question.