---

Convergence analysis of explicit stabilized integrators for parabolic semilinear stochastic PDEs.

---

A. Abdulle, C.-E. Bréhier, and G. Vilmart

---

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.

---

Key Words. explicit stabilized methods, second kind Chebyshev polynomials, stochastic partial differential equations, finite element methods.

---