Postprocessing for stochastic parabolic partial differential equations

Abstract. We investigate the strong approximation of stochastic parabolic partial differential equations with additive noise. We introduce post-processing in the context of a standard Galerkin approximation, although other spatial discretizations are possible. In time, we follow [20] and use an exponential integrator. We prove strong error estimates and discuss the best number of post-processing terms to take. Numerically, we evaluate the efficiency of the methods and observe rates of convergence. Some experiments with the implicit Euler–Maruyama method are described. Key words. Stochastic exponential integrator, post-processing, numerical solution of stochastic PDEs. AMS subject classifications. 60H15,65M12,65M15,65M60 1. Introduction. W