In this contribution, we provide convergence rates for a 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：本文研究了带有乘法Lipschitz噪声和齐次Neumann边界条件的随机热方程（SHE）有限体积格式的收敛速度。具体而言，针对SHE采用时间方向半隐式欧拉格式与空间方向TPFA格式的时空离散化，给出了其与SHE变分解在$L^2$范数下的误差估计。额外所需的唯一正则性假设是初始数据的空间正则性以及扩散项的光滑性。