A Finite Volume Method for a Convection-Diffusion Equation Involving a Joule Term

Abstract

This work is devoted to a Finite Volume method to approximate the solution of a convection-diffusion equation involving a Joule term. We propose a way to discretize this so-called "Joule effect" term in a consistent way with the non linear diffusion one, in order to ensure some maximum principle properties on the solution. We then investigate the numerical behavior of the scheme on two original benchmarks.