Space-time approximation of stochastic $p$-Laplace systems

TL;DR

This paper develops a finite-element based space-time approximation method for stochastic p-Laplace systems, achieving specific convergence rates by using a random time-grid to handle irregular time regularity.

Contribution

It introduces a novel space-time approximation approach with a random time-grid for stochastic p-Laplace systems, providing proven convergence rates under natural regularity assumptions.

Findings

Linear convergence in space.

Order α convergence in time for all α in (0, 1/2).

Numerical experiments confirm theoretical results.

Abstract

We consider systems of stochastic evolutionary equations of the $p$-Laplace type. We establish convergence rates for a finite-element based space-time approximation, where the error is measured in a suitable quasi-norm. Under natural regularity assumptions on the solution, our main result provides linear convergence in space and convergence of order $\alpha$ in time for all $\alpha\in(0,\frac{1}{2})$. The key ingredient of our analysis is a random time-grid, which allows us to compensate for the lack of time regularity. Our theoretical results are confirmed by numerical experiments.