Convergence analysis of explicit stabilized integrators for parabolic semilinear stochastic PDEs

TL;DR

This paper provides a comprehensive convergence analysis of explicit stabilized integrators combined with finite element methods for solving stiff parabolic semilinear stochastic PDEs, supported by numerical experiments.

Contribution

It offers the first fully discrete strong convergence analysis for these methods applied to stochastic PDEs with numerical validation.

Findings

Numerical experiments confirm theoretical convergence rates.

Explicit stabilized methods effectively handle stiff stochastic PDEs.

Finite element discretization complements the integrators for accurate solutions.

Abstract

Explicit stabilized integrators are an efficient alternative to implicit or semi-implicit methods to avoid the severe timestep restriction faced by standard explicit integrators applied to stiff diffusion problems. In this paper, we provide a fully discrete strong convergence analysis of a family of explicit stabilized methods coupled with finite element methods for a class of parabolic semilinear deterministic and stochastic partial differential equations. Numerical experiments including the semilinear stochastic heat equation with space-time white noise confirm the theoretical findings.