BUG: Multigrid doesn't work with a `MixedFunctionSpace` and a `Cofunction` right hand side. about firedrake

[pbrubeck]

I think we should address this issue by introducing a reconstruct(mesh) method for function spaces, and using it here, as @wence- suggested

firedrake/firedrake/mg/ufl_utils.py

Lines 149 to 152 in 4449d80

	if isinstance(V, firedrake.functionspaceimpl.FiredrakeDualSpace):
	V = firedrake.functionspace.DualSpace(mesh, V.ufl_element())
	else:
	V = firedrake.FunctionSpace(mesh, V.ufl_element())

[pbrubeck]

Also I don't think we have a @coarsen.register for MixedFunctionSpace

[JHopeCollins]

Also I don't think we have a @coarsen.register for MixedFunctionSpace

Does MixedFunctionSpace need it's own dispatch if the mixed-ness is being dealt with inside DualSpace and FunctionSpace?

[pbrubeck]

Does MixedFunctionSpace need it's own dispatch if the mixed-ness is being dealt with inside DualSpace and FunctionSpace?

I did not see why we should keep the impl.FunctionSpace dispatch, therefore there's no need to add one for impl.MixedFunctionSpace. These two are abstract classes that do not carry the actual geometry. The coarsen dispatch to deal with both primal and dual spaces on a mesh should be on WithGeometryBase.