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 $2$-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.