no. 4
Numerical approximation of stochastic time-fractional diffusion
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 53 (2019) no. 4, pp. 1245-1268

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 ∈ (0,1), and fractionally integrated Gaussian noise (with a Riemann-Liouville fractional integral of order γ ∈ [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.

Reçu le :
Accepté le :
DOI : 10.1051/m2an/2019025
Classification : 60H15, 60H35, 65M12
Keywords: stochastic time-fractional diffusion, Galerkin finite element method, Grünwald-Letnikov method, strong convergence, weak convergence

Jin, Bangti 1 ; Yan, Yubin 1 ; Zhou, Zhi 1

1 
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     title = {Numerical approximation of stochastic time-fractional diffusion},
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     pages = {1245--1268},
     year = {2019},
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Jin, Bangti; Yan, Yubin; Zhou, Zhi. Numerical approximation of stochastic time-fractional diffusion. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 53 (2019) no. 4, pp. 1245-1268. doi: 10.1051/m2an/2019025

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