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

04/05/2023

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by   Caroline Bauzet, et al.

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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))).