Stochastic exponential integrators for finite element discreitzation of SPDEs for multiplicative and additive noise

Gabriel James Lord, Antoine Tambue

Research output: Contribution to journalArticlepeer-review

52 Citations (Scopus)

Abstract

We consider the numerical approximation of a general second-order semilinear parabolic stochastic partial differential equation driven by multiplicative and additive space-time noise. We examine convergence of exponential integrators for multiplicative and additive noise. We consider noise that is in a trace class and give a convergence proof in the root-mean-square L-2 norm. We discretize in space with the finite element method and in our implementation we examine both the finite element and the finite volume methods. We present results for a linear reaction-diffusion equation in two dimensions as well as a nonlinear example of a two-dimensional stochastic advection-diffusion-reaction equation motivated from realistic porous media flow.

Original languageEnglish
Pages (from-to)515-543
Number of pages29
JournalIMA Journal of Numerical Analysis
Volume33
Issue number2
DOIs
Publication statusPublished - Apr 2013

Keywords

  • parabolic stochastic partial differential equation
  • finite element
  • exponential integrators
  • strong numerical approximation
  • multiplicative noise
  • additive noise
  • PARTIAL-DIFFERENTIAL-EQUATIONS
  • NUMERICAL-SIMULATION
  • APPROXIMATION
  • MATRIX
  • REGULARITY
  • SCHEME

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