In this contribution, we provide convergence rates for the finite volume scheme of the stochastic heat equation with multiplicative Lipschitz noise and homogeneous Neumann boundary conditions (SHE). More precisely, we give an error estimate for the $L^2$-norm of the space-time discretization of SHE by a semi-implicit Euler scheme with respect to time and a TPFA scheme with respect to space and the variational solution of SHE. The only regularity assumptions additionally needed is spatial regularity of the initial datum and smoothness of the diffusive term.

翻译：本文针对带有乘性Lipschitz噪声和齐次Neumann边界条件的随机热方程(SHE)，给出了其有限体积格式的收敛速度。具体而言，我们估计了SHE的半隐式Euler时间离散与TPFA空间离散所构成时空离散化格式的$L^2$范数误差，并将其与SHE的变分解进行比较。所需的额外正则性假设仅为初始数据的空间正则性以及扩散项的光滑性。