Numerical approximation of nonlinear fourth-order SPDEs with additive space-time white noise

TL;DR

This paper develops a spectral Galerkin and Euler scheme for numerically approximating a nonlinear fourth-order stochastic PDE driven by space-time white noise, achieving near-optimal convergence rates using stochastic sewing techniques.

Contribution

It introduces a full discretisation method for a complex nonlinear SPDE and proves its convergence with near-optimal rates, advancing numerical analysis for high-order stochastic PDEs.

Findings

Achieves almost spatial rate 1 convergence

Achieves 1-temporal rate convergence

Utilizes stochastic sewing technique for analysis

Abstract

We consider the strong numerical approximation for a fourth-order stochastic nonlinear SPDE driven by space-time white noise on $2$-dimensional torus. We consider its full discretisation with a spectral Galerkin scheme in space and Euler scheme in time. We show the convergence with almost spatial rate $1$ and $1$-temporal rate obtained mainly via \it{stochastic sewing} technique.