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

International audienceThe modelling of the heat diffusion coupled with electrical diffusion yields a nonlinear system of elliptic equations. The ohmic losses which appear as a source term in the heat diffusion equation is a nonlinear term which lies in $L^1$. 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