On the discretization of the coupled heat and electrical diffusion problems

Abstract

We consider a nonlinear system of elliptic equations, which arises when modelling the heat diffusion problem coupled with the electrical diffusion problem. The ohmic losses which appear as a source term in the heat diffusion equation yield a nonlinear term which lies in L1. A finite volume scheme is proposed for the discretization of the system; we show that the approximate solution obtained with the scheme converges, up to a subsequence, to a solution of the coupled elliptic system. © Springer-Verlag Berlin Heidelberg 2007.