Applying Boundary conditions to mixedspace

1

Dear Sir/ Ma’am
I want to apply boundary conditions (n cross E=0) to the nedelec element and I don’t want to apply any condition to the Lagrange element but both are in mixed space how can I come out of this problem. I can explain mathematically even better
let us assume E_t=0 and E_z is free at the boundary and

V=FiniteElement("Nedelec 1st kind H(curl)", triangle, 1)
    Q=FiniteElement("CG", triangle, 1)
    W=FunctionSpace(mesh, MixedElement([V,Q]))
    #Test and Trial FunctionS
    (e_t, e_z)=TrialFunctions(W)
    (v_t, v_z)=TestFunctions(W)

    pec=Expression(("0", "0"), degree=0) #only for nedelc element 
    bc1=DirichletBC(W, pec, boundary, 8)

and I know the above code will give an error since the dimension of the boundary condition does not match with the dimension of the space W

Here my doubt/question is how can I apply boundary condition to Nedelec element V sepeatley , even though nedelec element is part of the mixed element.

2

Use sub in the Dirichlet condition, as in the minimal working example below:

from dolfin import *
mesh = UnitSquareMesh(10, 10)

V=FiniteElement("Nedelec 1st kind H(curl)", triangle, 1)
Q=FiniteElement("CG", triangle, 1)
W=FunctionSpace(mesh, MixedElement([V,Q]))
#Test and Trial FunctionS
(e_t, e_z)=TrialFunctions(W)
(v_t, v_z)=TestFunctions(W)

pec=Expression(("0", "0"), degree=0) #only for nedelc element 
bc1=DirichletBC(W.sub(0), pec, "on_boundary")