Support for Function.assign on Submesh

[pbrubeck]

Describe the current issue
Currently Function.assign is not implemented across a Submesh and its parent.

Describe the solution you'd like
DOF-wise assignment of Functions with the same UFL element but on Submeshes should be trivial to implement by indexing.

MFE:

from firedrake import *
mesh = UnitSquareMesh(2, 2)
M = FunctionSpace(mesh, "DG", 0)
m = Function(M)
m.dat.data[0] = 1

rmesh = RelabeledMesh(mesh, [m], [100])
submesh = Submesh(rmesh, rmesh.geometric_dimension(), 100)

V = FunctionSpace(rmesh, "DG", 0)
Vsub = V.reconstruct(mesh=submesh)
u = Function(V)
usub = Function(Vsub)
usub.assign(1)

u.assign(usub, subset=rmesh.cell_subset(100))
print(u.dat.data)

Error message:

Traceback (most recent call last):
  File "/home/pbrubeck/git/dphil_thesis/static_condensation/snippets/bug_submesh_assign.py", line 16, in <module>
    u.assign(usub, subset=rmesh.cell_subset(100))
  File "petsc4py/PETSc/Log.pyx", line 188, in petsc4py.PETSc.Log.EventDecorator.decorator.wrapped_func
  File "petsc4py/PETSc/Log.pyx", line 189, in petsc4py.PETSc.Log.EventDecorator.decorator.wrapped_func
  File "/home/pbrubeck/firedrake/src/firedrake/firedrake/adjoint_utils/function.py", line 116, in wrapper
    ret = assign(self, other, *args, **kwargs)
  File "/home/pbrubeck/firedrake/src/firedrake/firedrake/function.py", line 461, in assign
    Assigner(self, expr, subset).assign()
  File "/home/pbrubeck/firedrake/src/firedrake/firedrake/assign.py", line 155, in __init__
    raise ValueError("All functions in the expression must use the same "
ValueError: All functions in the expression must use the same mesh as the assignee

Describe alternatives you've considered
Function.interpolate works with Submesh, but does redundant work by evaluating the degrees of freedom of the element on itself. This of course will fail for elements where dual evaluation is not implemented.

Additional info
Add any other information here.