Convergence of a finite-volume scheme for a heat equation with a multiplicative Lipschitz noise

International audienceWe study here the approximation by a finite-volume scheme of a heat equation forced by a Lipschitz continuous multiplicative noise in the sense of Itô. More precisely, we consider a discretization which is semi-implicit in time and a two-point flux approximation scheme (TPFA) in space. We adapt the method based on the theoremof Prokhorov to obtain a convergence in distribution result, then Skorokhod'srepresentation theorem yields the convergence of the scheme towards a martingalesolution and the Gyöngy-Krylov argument is used to prove convergence in probabilityof the scheme towards the unique variational solution of our parabolic problem