A splitting/polynomial chaos expansion approach for stochastic evolution equations

Abstract

In this paper, we combine deterministic splitting methods with a polynomial chaos expansion method for solving stochastic parabolic evolution problems. The stochastic differential equation is reduced to a system of deterministic equations that we solve efficiently by splitting methods. The method can be applied to a wide class of problems where the related stochastic processes are given uniquely in terms of stochastic polynomials. A comprehensive convergence analysis is provided and numerical experiments validate our approach.

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Acknowledgements

This work was partially supported by a Research grant for Austrian graduates granted by the Office of the Vice Rector for Research of University of Innsbruck. The computational results presented have been partially achieved using the HPC infrastructure LEO of the University of Innsbruck. A. Kofler was supported by the program Nachwuchsförderung 2014 at University of Innsbruck. H. Mena was supported by the Austrian Science Fund—Project Id: P27926. We thank the anonymous referee for his/her valuable comments that helped greatly to improve this work.

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Correspondence to Tijana Levajković.

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Kofler, A., Levajković, T., Mena, H. et al. A splitting/polynomial chaos expansion approach for stochastic evolution equations. J. Evol. Equ. (2020). https://doi.org/10.1007/s00028-020-00627-5

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Mathematics Subject Classification

  • 60H35
  • 65M75
  • 65J10
  • 60H40
  • 65M12
  • 11B83

Keywords

  • Splitting methods
  • Analytic semigroups
  • Resolvent splitting
  • Polynomial chaos expansion
  • Fourier–Legendre polynomials
  • Wiener–Legendre expansion