Discretization of the coupled heat and electrical diffusion problems by the finite element and the finite volume methods

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 couples both equations. A finite element scheme and a finite volume scheme are considered for the discretization of the system; in both cases, we show that the approximate solution obtained with the scheme converges, up to a subsequence, to a solution of the coupled elliptic system.