Convergence of a TPFA scheme for a diffusion-convection equation with a multiplicative stochastic noise

The aim of this paper is to address the convergence analysis of a finite-volume scheme for the approximation of a stochastic non-linear parabolic problem set in a bounded domain of R 2 and under homogeneous Neumann boundary conditions. The considered discretization is semi-implicit in time and TPFA in space. By adapting well-known methods for the time-discretization of stochastic PDEs, one shows that the associated finite-volume approximation converges towards the unique variational solution of the continuous problem strongly in L 2 (Ω; L 2 (0, T ; L 2 (Λ)))