Petrov-Galerkin Formulations in Firedrake

[mfeuerle]

I have a short question: is Firedrake naturally able to handle Petrov-Galerkin formulations, i.e. variational formulations where Trial and Test space are not equal (and may incorporate different Dirichlet BCs on different boundary parts), e.g. something like

U = FunctionSpace(mesh, "CG", 3)
V = FunctionSpace(mesh, "CG", 1)

u = TrialFunction(U)
v = TestFunction(V)

uD = ...
vD = ...

bcs = [DirichletBC(U, uD, 1),
       DirichletBC(V, vD, 2)]

A = ...
l = ...

sol = Function(U)
solve(A == l, sol, bcs=bcs)

For Fenicsx there is no support for that (it is possible, but you have to handle the BCs by modifying the linear system in PETSc or NumPy manually), and i also found nothing when searching for NGSolve (although i only tried Fenicsx).
So my question is not, if that is somehow possible using Firedrake, but if that is already supported out of the box (-> possible without manually fiddling with the linear system).

Maybe see https://fenicsproject.discourse.group/t/petrov-gelerkin-formulations-and-fenicsx/18369?u=mfeuerle for the original question on the Fenicsx forum.

I guess it is not supported according to this #3502 (comment), but it was also stated here #197 (comment), that there are thoughts on adding support.

[connorjward]

There is this PR that claims to add support for this. However the author is no longer working actively on this so it is unlikely to be merged unless someone takes it up again.

[mfeuerle]

Okay, thanks for the answer :D