AffiliationUniversity of Chester; University College London; The Hong Kong Polytechnic University
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AbstractWe 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.
CitationJin, B., Yan, Y. & Zhou, Z. (2019). Numerical approximation of stochastic time-fractional diffusion. ESAIM: M2AN, 53(4), 1245-1268
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