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Explicit stabilized integrators are an efficient alternative to implicit orsemi-implicit methods to avoid the severe timestep restriction faced bystandard explicit integrators applied to stiff diffusion problems. In thispaper, we provide a fully discrete strong convergence analysis of a family ofexplicit stabilized methods coupled with finite element methods for a class ofparabolic semilinear deterministic and stochastic partial differentialequations. Numerical experiments including the semilinear stochastic heatequation with space-time white noise confirm the theoretical findings.

Convergence analysis of explicit stabilized integrators for parabolic semilinear stochastic PDEs