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I want to calculate the electrostatic potential for an two-dimensional area with given Dirichlet boundary conditions (say, a square) with a charged ring in it (like a wedding ring, but inifinitely thin) with a given line charge density. I figured out that the problem should be solvable if I divided up the whole area into two areas: inside (solution phi_1(r)) and outside (solution phi_2(r)) the ring, connected with the boundary conditions

phi_1=phi_2

dphi_1/dn-dphi_2/dn=\sigma/epsilon_0

d.../dn is the normal derivative, and sigma is the position-dependent line charge along the ring.

If you want, you can also think about the physics behind this, but my real question is about the mathematical issue: Do you know any (free) FEM software that can implement those conditions? I read into NGsolve and ELMER until now, and I don't think they can do it (at least, in a reasonable amout of my time configuring it).

Best

Rafael

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# FEM software? Poisson equation: Boundary conditions for a charged boundary

Can you offer guidance or do you also need help?

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