How to set the boundary conditions of conductors with unknown potential when solving the potential distribution

[sbhasan]

A simple way is to model the boundary as a thin layer with very high dielectric constant.

If you prefer to solve it in a more nifty way, there was a past discussion in which Nitsche’s method was used to enforce this constraint. If interested, you can read it here:

Impose electric current magnitude / Floating potential

Dear all, I’m working on a static electric conduction problem, governed by a simple Poisson equation: -\nabla \cdot [\sigma(x,y)\nabla u(x,y)] = 0 with \sigma the electric conductivity and u the electric potential. I understand that if I impose Dirichlet Boundary Conditions (BC) on a boundary, the electric potential u will be fixed on this boundary, while a Neumann BC will impose \frac{\delta u}{\delta n} on the boundary (with n the normal vector to the boundary). For a known conductivity …