Numerical approximation of stochastic time-fractional diffusion

Bangti Jin, Yubin Yan, Zhi Zhou

Research output: Journal article publicationJournal articleAcademic researchpeer-review

29 Citations (Scopus)


We develop and analyze a numerical method for stochastic time-fractional diffusion driven by additive fractionally integrated Gaussian noise. The model involves two nonlocal terms in time, i.e., a Caputo fractional derivative of order α â (0,1), and fractionally integrated Gaussian noise (with a Riemann-Liouville fractional integral of order γ â [0,1] in the front). The numerical scheme approximates the model in space by the standard Galerkin method with continuous piecewise linear finite elements and in time by the classical Grünwald-Letnikov method (for both Caputo fractional derivative and Riemann-Liouville fractional integral), and the noise by the L2-projection. Sharp strong and weak convergence rates are established, using suitable nonsmooth data error estimates for the discrete solution operators for the deterministic inhomogeneous problem. One- and two-dimensional numerical results are presented to support the theoretical findings.

Original languageEnglish
Pages (from-to)1245-1268
Number of pages24
JournalESAIM: Mathematical Modelling and Numerical Analysis
Issue number4
Publication statusPublished - 9 Jul 2019


  • Galerkin finite element method
  • Grünwald-Letnikov method
  • Stochastic time-fractional diffusion
  • Strong convergence
  • Weak convergence

ASJC Scopus subject areas

  • Analysis
  • Numerical Analysis
  • Modelling and Simulation
  • Computational Mathematics
  • Applied Mathematics


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