Add interior point to Dirichlet Boundary

mesh
1

Hello,

I want to add an interior point in my domain Omega to the Dirichlet boundary. For example, the code below solves a PDE with Dirichlet Boundary Gamma = [1,0]x{0} v [1,0]x{1} v {0}x[1,0] v {1} x [1,0]. I want to add the origin to the boundary, that is, the boundary should read Gamma v {(0,0)}. Is this possible?

=================================================================

from dolfin import *
import matplotlib.pyplot as plt
mesh=UnitSquareMesh(4,4)
V = FunctionSpace(mesh,‘P’,1)
bc = DirichletBC(V,Constant(0.0),“on_boundary”)
f = Constant(1.0)
u = TrialFunction(V)
v = TestFunction(V)
a = dot(grad(u), grad(v))dx
L = fv*dx
u_h = Function(V)
solve(a == L, u_h, bc)

plot(u_h)
plot(mesh)
plt.show()

=================================================================

2

from dolfin import *
import matplotlib.pyplot as plt
mesh=UnitSquareMesh(4,4)
V = FunctionSpace(mesh,‘P’,1)
bc = DirichletBC(V,Constant(0.0),“on_boundary”)
f = Constant(1.0)
u = TrialFunction(V)
v = TestFunction(V)
a = dot(grad(u), grad(v)) * dx
L = f * v * dx
u_h = Function(V)
solve(a == L, u_h, bc)
plot(u_h)
plot(mesh)
plt.show()