Convergence analysis of explicit stabilized integrators for parabolic semilinear stochastic PDEs

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.

Assyr Abdulle passed away on September 1st, 2021 prior to the revision of this paper. To appear in IMA Journal of Numerical Analysis

References in corpus (2)

• Analysis of Some Splitting Schemes for the Stochastic Allen-Cahn Equation
• Optimal explicit stabilized integrator of weak order one for stiff and ergodic stochastic differential equations