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The aim of this paper is to address the convergence analysis of afinite-volume scheme for the approximation of a stochastic non-linear parabolicproblem set in a bounded domain of $\mathbb{R}^2$ and under homogeneous Neumannboundary conditions. The considered discretization is semi-implicit in time andTPFA in space. By adapting well-known methods for the time-discretization ofstochastic PDEs, one shows that the associated finite-volume approximationconverges towards the unique variational solution of the continuous problemstrongly in $L^2(\Omega; L^2(0,T;L^2(\Lambda)))$.

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