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 $\mathbb{R}^2$ 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 $L^2(\Omega; L^2(0,T;L^2(\Lambda)))$.

翻译：本文旨在研究有界区域$\mathbb{R}^2$上、齐次Neumann边界条件下随机非线性抛物型问题逼近的有限体积格式的收敛性分析。所考虑的离散格式在时间上采用半隐式，在空间上采用TPFA格式。通过改编随机偏微分方程时间离散的经典方法，我们证明了相应的有限体积逼近在$L^2(\Omega; L^2(0,T;L^2(\Lambda)))$意义下强收敛于连续问题的唯一变分解。