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

Abstract

In this talk we discuss the numerical approximation of the stochastic $p$-Laplace system. In general non-linear as well as stochastic equations have limited regularization properties. Therefore, solutions do not enjoy arbitrary high regularity. This leads to severe difficulties in the error analysis for existing discretization schemes. We propose a new numerical scheme based on the approximation of time averaged values of the (unknown) solution. We verify optimal convergence of rate 1/2 in time and 1 in space under realistic regularity requirements. Additionally, we provide a sampling algorithm that approximates the non-standard stochastic input data. This is joint work with Lars Diening (Bielefeld, Germany) and Martina Hofmanová (Bielefeld, Germany).