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

Abstract

We consider the strong numerical approximation for a fourth-order stochastic nonlinear SPDE driven by space-time white noise on {$d=1,2,3$}-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 $2-\frac{d}{2}$ and $\frac{6-d}{4}$-temporal rate obtained mainly via \it{Stochastic Sewing} technique.

21 pages