mixed spaces over different meshes

Question

Hi,
I have a basic question related to the old one of http://fenicsproject.org/qa/1216/linear-dependent-basis-function-on-fenics-formulations.
I can not understand the relationship of global functions of two different meshes on
the assembled system matrix. The code below illustrates my point.

from dolfin import *

mesh1 = UnitIntervalMesh(4)
mesh2 = UnitIntervalMesh(2)

V1 = FunctionSpace(mesh1, "CG", 2)    # 9 Lagrange global functions of degree 2
V2 = FunctionSpace(mesh2, "CG", 1)    # 3 Lagrange global functions of degree 1

V = V1 * V2

(u1, u2) = TrialFunctions(V)
v1 = TestFunction(V1)

a =  (inner(grad(u1), grad(v1)) * dx) + (inner(grad(u2), grad(v1)) * dx) 
A = assemble(a)

V1_dofs = V.sub(0).collapse(mesh1)[1].values()
V2_dofs = V.sub(1).collapse(mesh2)[1].values()

print 'V1 dofs = ', V1_dofs
print 'V2 dofs = ', V2_dofs

print 'A = ', A.array()

I would expect to find three V2 dofs associated with the functions of space V2. Mesh2 has
only 3 nodes. But there are five V2 dofs = [4, 2, 6, 9, 13]. There is no problem with
V1 dofs = [0, 1, 3, 5, 7, 8, 10, 11, 12]. There are 5 mesh nodes and
the midpoints of its elements. The assembled system matrix don't have 12 columns. I can t
understand it. Any help will be appreciated.
Thanks for availability.

Comments

Please try to use the proper formatting. You have then a better chance to obtain an answer.

Answer 1

As far as I know you cannot have a mixed space of function spaces defined on different meshes. There mistake should have been captured, though, so looks to me like a bug. Please correct me if I'm wrong?

Comments

Mikael, thank you for the feedback. Is not possible to do this with nested meshes / hierarchically related Function spaces? I am not completely convinced that it is impossible.
Any help about this dofs relations would be appreciated.

---

This is from line 483 of site-packages/functions/functionspace.py:

    #if not all(V.mesh() == spaces[0].mesh() for V in spaces):
    #    cpp.dolfin_error("functionspace.py", "Nonmatching meshes for mixed function space: " \
    #              + str([V.mesh() for V in spaces]))

Don't know why it's commented out. Uncommented it would catch your effort to create a mixed space with two different meshes. You could post a question on why on the fenics mailinglist or report a bug (that your mixed space is created) on bitbucket.

---

Using FEniCS >= 1.5 and this multimesh or mshr functionalities
is possible to assemble a form a over two distict meshes
(hierarquicaly related)?