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：本文针对具有乘性Lipschitz噪声及齐次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率。具体而言，我们通过半隐式Euler时间离散格式和TPFA空间离散格式，对SHE的时空离散化与变分解之间的$L^2$范数误差进行了估计。除初始条件的空间正则性和扩散项的光滑性外，该分析无需额外的正则性假设。