An averaged space-time discretization of the stochastic $p$-Laplace system

TL;DR

This paper introduces two novel space-time discretization methods for the stochastic p-Laplace system, achieving linear spatial and half-order temporal convergence, supported by an efficient sampling algorithm and numerical validation.

Contribution

The paper presents new discretization schemes based on time-averaged values for the stochastic p-Laplace system, with proven convergence rates and an efficient sampling algorithm.

Findings

Linear convergence in space

Half-order convergence in time

Numerical experiments confirm theoretical results

Abstract

We study the stochastic $p$-Laplace system in a bounded domain. We propose two new space-time discretizations based on the approximation of time-averaged values. We establish linear convergence in space and $1/2$ convergence in time. Additionally, we provide a sampling algorithm to construct the necessary random input in an efficient way. The theoretical error analysis is complemented by numerical experiments.