Affiliation
University of Chester; University College London; The Hong Kong Polytechnic UniversityPublication Date
2019-07-09
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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 $\alpha\in(0,1)$, and fractionally integrated Gaussian noise (with a Riemann-Liouville fractional integral of order $\gamma \in[0,1]$ 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 Gr\"unwald-Letnikov method, and the noise by the $L^2$-projection. Sharp strong and weak convergence rates are established, using suitable nonsmooth data error estimates for the deterministic counterpart. One- and two-dimensional numerical results are presented to support the theoretical findings.Citation
Jin, B., Yan, Y. & Zhou, Z. (2019). Numerical approximation of stochastic time-fractional diffusion. ESAIM: M2AN, 53(4), 1245-1268Publisher
EDP SciencesJournal
ESAIM: M2ANType
ArticleEISSN
1290-3841Collections
Except where otherwise noted, this item's license is described as http://creativecommons.org/licenses/by-nc-nd/4.0/