← Back to team overview

dolfin team mailing list archive

Laplace equation in 2D

 

Dear Dolfin developers

I am trying to learn to use dolfin for a relatively simple
problem, but there are a couple of things that I haven't been able
to figure out from the manual.
What I am trying to do is solving Laplace equation in the geometry
illustrated below (in 2D) in order to find the electrostatic potential:
          _________
          |       |
          |       |
 _________|_______|_________
 |       Dielectric         |
 |__________________________|
          V = const

I have Dirichlet BC on all boundaries.

1) How do you deal with the internal boundary between the dielectric
    and vacuum in FEM ? Here the solution has a discontinuity in the
    normal derivative.
2) The variational form of Laplace equation is:
            a = dot(grad(v), grad(u))*dx = 0
     However, the LinearPDE function takes both an "a" and an "L"
     (see eg the poisson demo.py). What am I missing here ?
3) Having obtained a solution, how do I get its value at an arbitrary
   position ? Have tried the eval attribute, but it complains about
   the input type (I tried with an array).

I hope that you have time to clarify these things for me.
Thanks in advance.
Kristen Kaasbjerg

PS: I am using the python wrappers.