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[Johan Hake <hake.dev@xxxxxxxxx>]

You can read more in detail about this in the FEniCS book. Search for
DirichletBC. You can also get some usefull information by

>>> help(DirichletBC)

in a Python session.

As far as I can see there is nothing wrong with your script.

Johan

On 11/29/2012 03:55 AM, Huadong GAO wrote:
> Question #215444 on UFL changed:
> https://answers.launchpad.net/ufl/+question/215444
> 
>     Status: Answered => Open
> 
> Huadong GAO is still having a problem:
> First thanks Johan's help.   A simple python code is attached below. I use quadratic element
> solving Poisson Equation on the UnitCircle domain, I do not know how FEniCS apply the Dirichlet boundary conditions. I mean the how to determine the value at the midpoint of the boundary edge ?
> 
> ######################################
> from dolfin import *
> 
> mesh = UnitCircle(5)
> V = FunctionSpace(mesh, "Lagrange", degree=2)
> 
> u = TrialFunction(V)
> v = TestFunction(V)
> 
> #--------------------------------------------
> f = Expression("1.0")
> u_e = Expression("exp(x[0]+x[1]-t)",t=0)
> #--------------------------------------------
> 
> a = inner(nabla_grad(u),nabla_grad(v))*dx
> v = f*v*dx
> 
> def boundary(x,on_boundary):
>     return on_boundary
> 
> bc = DirichletBC(V,u_e,boundary)
> 
> A = assemble(a)
> b = assemble(v)
> bc.apply(A,b)
> u = Function(V)
> solver = KrylovSolver("gmres", "ilu")            
> solver.solve(A, u.vector(), b)
> 
> plot(mesh)
> plot(u)
> interactive()
> ######################################
>