Zero Dirichlet Boundary Condition doesn't work

Question

I have just reinstalled the newest version of FEniCS, and try to rerun some previous code. However, I keep getting some different results and finally I find the problem is from the boundary condition.

Here is my code:

V = FunctionSpace(mesh, "Lagrange", 1)

def boundary(x, on_boundary):
    return on_boundary
u0 = Constant(0.0)
bc = DirichletBC(V, u0, boundary)

u = TrialFunction(V)
v = TestFunction(V)    
res = Function(V)

a = 0.5*inner(nabla_grad(u), nabla_grad(v))*dx-u*r*v*dx
b = v*dx

problem = LinearVariationalProblem(a, b, res, bc)
solver = LinearVariationalSolver(problem)
solver.parameters["linear_solver"] = "gmres"
solver.parameters["preconditioner"] = "amg"
solver.solve()

The mesh I used is adaptive. And I find the calculated result $res$ doesn't satisfy zero boundary condition.

Comments

bc is not defined in your code

---

I am sorry I forget to post the code of setting bc

u0 = Constant(0.0)
bc = DirichletBC(V, u0, boundary)

Answer 1

Hi,

What is your space V?

For instance, if V = DG1, your solution may not be equal to 0 on the boundary even if you use 0 dirichlet BC (because of the discontinuity of the solution, it will be 0 on the outside facet of the boundary but res will only contain the value on the inside of the boundary)

Comments

Here is the V:

V = FunctionSpace(mesh, "Lagrange", 1)

Answer 2

My initial mesh is

mesh = BoxMesh(-50,-50,-50,50,50,50,2,2,2)

Then I create an adaptive mesh from the initial mesh based on some conditions, and conduct the calculation in the original post. Here is an example that the calculated result $res$ doesn't satisfy zero boundary condition.

res[-50,25,-25]=0.0188,

where it should be zero because it is on the boundary.

Answer 3

I did another test on the same problem with a rougher mesh, and here are results on boundary:

[-50. -50. -50.] 0.0
[  0. -50. -50.] 0.0
[ 50. -50. -50.] 0.0
[-50.   0. -50.] 0.0
[  0.   0. -50.] 0.0
[ 50.   0. -50.] 0.0
[-50.  50. -50.] 0.0
[  0.  50. -50.] -0.000258264961087
[ 50.  50. -50.] 0.0
[-50. -50.   0.] 0.0
[  0. -50.   0.] -0.000138253282976
[ 50. -50.   0.] 0.0
[-50.   0.   0.] -0.00013825329051
[ 50.   0.   0.] 0.0
[-50.  50.   0.] -0.000258009737271
[  0.  50.   0.] 0.00651775683023
[ 50.  50.   0.] -0.000261577716232
[-50. -50.  50.] 0.0
[  0. -50.  50.] -0.000138253291081
[ 50. -50.  50.] 0.0
[-50.   0.  50.] 0.0
[  0.   0.  50.] -0.000138253339378
[ 50.   0.  50.] 0.0
[-50.  50.  50.] 0.0
[  0.  50.  50.] 0.0
[ 50.  50.  50.] 0.0

where all the boundary values should be zero??

I tested the same problem on FEniCS 1.1, and the results are zero at these boundary points.