Dirichlet boundary condition fail in DG simulation

Question

Can anyone explain why the Dirichlet Boundary conditions don't kick in in my dg simulation of the linear scalar wave equation? How can I fix this? Thanks in advance.

My dg code:

from dolfin import *

# Constants
D     = 2.0*DOLFIN_PI
lmbda = 0.5*D
l     = D/lmbda
omega = -D*D/lmbda

# Prepare a mesh
mesh = IntervalMesh(50, 0.0, D)

# Define function spaces
DGorder = 1
V = FunctionSpace(mesh, "DG", DGorder)
U = FunctionSpace(mesh, "DG", DGorder)

# Set some expressions
uinit = Expression("0")
ubdr  = Expression("sin(l*x[0]-omega*t)", l = l, omega = omega, t = 0.0)

# Set boundary conditions
Port = CompiledSubDomain("near(x[0], 0.0)")
bc   = DirichletBC(U, ubdr, Port)

# Set initial values
u0 = interpolate(uinit, U)

# Define test and trial functions
v = TestFunction(V)
u = TrialFunction(U)

# Set time stepping parameters
t  = 0
dt = 0.001
T  = DOLFIN_PI

# Define normals
n = FacetNormal(mesh)

# Set penalty parameter
alpha = 1.

# Central differences for time and spatial discretisation
udot = (u - u0)/dt
uold = (u + u0)*0.5

# Define fluxes on interior and exterior facets
uhat    = avg(D*uold) + D*(1.-alpha)*0.5*jump(uold)
uhatbnd = D*uold      + D*(1.-alpha)*0.5*uold

# Define variational formulation
F =   (udot*v - D*uold*v.dx(0))*dx \
    + uhat * jump(v)*dS \
    + uhatbnd * v*ds

a, L = lhs(F), rhs(F)

# Prepare solution
u = Function(U)
plot(u0)

# The acutal timestepping
while t < T:
    ubdr.t = t
    solve(a == L, u, bcs = bc)
    u0.assign(u)
    t += dt
    plot(u0)

Answer 1

Hi, the DirichletBC object in your code finds no degrees of freedom to prescribe the boundary condition. If you change the search method to "pointwise" the code will work as intended, that is

bc   = DirichletBC(U, ubdr, Port, "pointwise")