Apply heat flux in different function space

1

Dear all,

I am hoping to apply a heatFlux in a DG0 function space as opposed to a CG1 function space:

Here is an MWE:

from fenics import *

mesh = BoxMesh.create(MPI.comm_world,[Point(0, 0, 0), Point(1,1,1)],[10,10,10],CellType.Type.hexahedron) 

class negX(SubDomain):
    def inside(self, x, on_boundary):
        return near(x[0], Constant(0.0))
    
class posX(SubDomain):
    def inside(self, x, on_boundary):
        return near(x[0], Constant(1.0))
    
negX = negX(); posX = posX();
    
Surfaces = MeshFunction('size_t', mesh, 2)
Surfaces.set_all(0)
negX.mark(Surfaces, 1)
posX.mark(Surfaces, 2)
ds = Measure("ds")(subdomain_data=Surfaces)

A = FunctionSpace(mesh, "CG", 1)
B = FunctionSpace(mesh, "DG", 0)

Tn = Function(A)
Tn_plus_1 = Function(A)

timeStep = 1
heatFlux = 1
for i in range(1, 10): 
    
    ##############################################################################
    #Transient-heat
    
    #Test & Trial functions (Temperature)
    uA = TrialFunction(A)
    vA = TestFunction(A)
    
    uB = TrialFunction(B)
    vB = TestFunction(B)
    
    #Form (Temperature)
    thermalForm = uA*vA*dx - Tn*vA*dx + Constant(timeStep)*inner(grad(uA),grad(vA))*dx - Constant(timeStep)*inner(heatFlux,vB)*ds(2)
    a = lhs(thermalForm)
    L = rhs(thermalForm)
    
    #Solve
    solve(a == L, Tn_plus_1)
    
    #Update
    Tn.assign(Tn_plus_1)
    
File('T.pvd') << Tn_plus_1

However I am getting the following error:

UFLException: Found different Arguments with same number and part.
Did you combine test or trial functions from different spaces?
The Arguments found are:
  v_1
  v_0
  v_0

Is there a way to solve this problem using two different function spaces?

Many thanks