Convergence rates for a finite volume scheme of a stochastic non-linear parabolic equation

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