MATHICSE-GroupAbdulle, AssyrBréhier, Charles-EdouardVilmart, Gilles2021-02-162021-02-162021-02-162021-02-0510.5075/epfl-MATHICSE-283314https://infoscience.epfl.ch/handle/20.500.14299/175304Explicit 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.explicit stabilized methodssecond kind Chebyshev polynomialsstochastic partial differential equationsfinite element methodstext::working paper