Yan, YubinJin, BangtiZhou, Zhi2019-10-082019-10-082019-07-09Jin, B., Yan, Y. & Zhou, Z. (2019). Numerical approximation of stochastic time-fractional diffusion. ESAIM: M2AN, 53(4), 1245-1268http://hdl.handle.net/10034/622682We 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.http://creativecommons.org/licenses/by-nc-nd/4.0/stochastic time-fractional diffusionGalerkin finite element methodstrong convergenceweak convergenceArticle1290-3841ESAIM: M2AN