Defining BC in Mixed formulation for Poisson equation

dolfinx
1

Hi,
I’m trying to adapt this tutorial from fenics to dolfinx, but I’m struggling in the definition of the Dirichlet BCs.
Please, find below the code:

from dolfinx import mesh, fem
import ufl
from mpi4py import MPI
import numpy as np
from petsc4py import PETSc

domain = mesh.create_unit_square(MPI.COMM_WORLD, 8, 8, mesh.CellType.triangle)

# Mixed function space
BDMe = ufl.FiniteElement("BDM", domain.ufl_cell(), 1)
DGe = ufl.FiniteElement("DG", domain.ufl_cell(), 1)

BDM = fem.FunctionSpace(domain, BDMe)
DG = fem.FunctionSpace(domain, DGe)
W = fem.FunctionSpace(domain, ufl.MixedElement([BDMe, DGe]))

# Define test and trial functions
(sigma, u) = ufl.TrialFunctions(W)
(tau, v) = ufl.TestFunctions(W)

# define source term
x = ufl.SpatialCoordinate(domain)
f =  10 * ufl.exp(-((x[0] - 0.5)**2 + (x[1] - 0.5)**2) / 0.02)

# variational form
a = (ufl.dot(sigma, tau) + ufl.div(tau)*u + ufl.div(sigma)*v)*ufl.dx
L = - f*v*ufl.dx

# Define boundary space
class BoundarySource(fem.Expression):
    def __init__(self, mesh):
        self.mesh = mesh
    def eval_cell(self, values, x, ufc_cell):
        cell = ufl.Cell(self.mesh, ufc_cell.index)
        n = cell.normal(ufc_cell.local_facet)
        g = np.sin(5*x[0])
        values[0] = g*n[0]
        values[1] = g*n[1]
    def value_shape(self):
        return (2,)

G = BoundarySource(domain)

side_facets = mesh.locate_entities_boundary(domain, 1, lambda x: (np.isclose(x[1], 0.0) | np.isclose(x[1], 1.0)))
bdofs = fem.locate_dofs_topological(BDM, 1, side_facets)

bc = fem.dirichletbc(G, bdofs)

Does anybody know what I am doing wrong?
I guess that the problem is the definition of the BoundarySource class, but I don’t know how to modify it correctly.

Thanks in advance!

2

Have you had a look at: Unable to apply dirichlet BC in mixed formulation - #2 by dokken
and the subsequent example?

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