# Mixed elements with two different meshes

I am interested in a finite element formulation using two variables, which are sought in finite element spaces with different meshes.

Here is code for a contrived example:

# coarse mesh space

mesh = UnitSquare(1,1)

V = FunctionSpace(mesh, 'CG', 1)

# fine mesh space

mesh.refine()

W = FunctionSpace(mesh, 'CG', 1)

# product space

X = V + W

I would have thought that this resulted in a coarse mesh space (dimension 4) for the V variable and a finer mesh space

(dimension 9) for the W variable, so that the space X would have dimension 13. However this is not what happens, as

can be seen by printing the results:

-------> print(V)

<Function space of dimension 4 (<CG1 on a <triangle of degree 1>>)>

-------> print(W)

<Function space of dimension 9 (<CG1 on a <triangle of degree 1>>)>

-------> print(X)

<Function space of dimension 18 (<Mixed element: (<CG1 on a <triangle of degree 1>>, <CG1 on a <triangle of degree 1>>)>)>

Is it possible to accomplish what I am trying to do: have mixed elements with different meshes for the different components?

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