Postprocessing for stochastic parabolic partial differential equations

Gabriel J. Lord, Tony Shardlow

Research output: Contribution to journalArticle

22 Citations (Scopus)

Abstract

We investigate the strong approximation of stochastic parabolic partial differential equations with additive noise. We introduce postprocessing in the context of a standard Galerkin approximation, although other spatial discretizations are possible. In time, we follow [G. J. Lord and J. Rougemont, IMA J. Numer. Anal., 24 (2004), pp. 587-604] and use an exponential integrator. We prove strong error estimates and discuss the best number of postprocessing 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. © 2007 Society for Industrial and Applied Mathematics.

Original languageEnglish
Pages (from-to)870-889
Number of pages20
JournalSIAM Journal on Numerical Analysis
Volume45
Issue number2
DOIs
Publication statusPublished - 2007

Keywords

  • Numerical solution of stochastic PDEs
  • Postprocessing
  • Stochastic exponential integrator

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