Postprocessing for stochastic parabolic partial differential equations

Tony Shardlow, Gabriel Lord

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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.
Original languageEnglish
Pages (from-to)870-889
Number of pages20
JournalSIAM Journal on Numerical Analysis (SINUM)
Volume45
Issue number2
Early online date27 Apr 2007
DOIs
Publication statusPublished - 30 Apr 2007

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