Strong approximation of monotone stochastic partial differential equations driven by white noise

Zhihui Liu, Zhonghua Qiao

Research output: Journal article publicationJournal articleAcademic researchpeer-review

10 Citations (Scopus)

Abstract

We establish an optimal strong convergence rate of a fully discrete numerical scheme for second-order parabolic stochastic partial differential equations with monotone drifts, including the stochastic Allen-Cahn equation, driven by an additive space-time white noise. Our first step is to transform the original stochastic equation into an equivalent random equation whose solution possesses more regularity than the original one. Then we use the backward Euler in time and spectral Galerkin in space to fully discretise this random equation. By the monotonicity assumption, in combination with the factorisation method and stochastic calculus in martingale-type 2 Banach spaces, we derive a uniform maximum norm estimation and a Hölder-type regularity for both stochastic and random equations. Finally, the strong convergence rate of the proposed fully discrete scheme is obtained. Several numerical experiments are carried out to verify the theoretical result.

Original languageEnglish
Pages (from-to)1074-1093
Number of pages20
JournalIMA Journal of Numerical Analysis
Volume40
Issue number2
DOIs
Publication statusPublished - Apr 2020

Keywords

  • backward Euler-spectral Galerkin scheme
  • martingale-type 2 Banach space
  • monotone stochastic partial differential equations
  • strong convergence rate

ASJC Scopus subject areas

  • Mathematics(all)
  • Computational Mathematics
  • Applied Mathematics

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