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Numerical Approximation of Stochastic Time-Fractional Diffusion
Yan, Yubin Jin, Bangti Zhou, Zhi
Yan, Yubin
Jin, Bangti
Zhou, Zhi
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2019-07-09
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Abstract
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), 1245-1268
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EDP Sciences
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ESAIM: M2AN
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Article
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1290-3841