Numerical Approximation of Stochastic Time-Fractional Diffusion
dc.contributor.author | Yan, Yubin | |
dc.contributor.author | Jin, Bangti | |
dc.contributor.author | Zhou, Zhi | |
dc.date.accessioned | 2019-10-08T08:55:26Z | |
dc.date.available | 2019-10-08T08:55:26Z | |
dc.date.issued | 2019-07-09 | |
dc.identifier.citation | Jin, B., Yan, Y. & Zhou, Z. (2019). Numerical approximation of stochastic time-fractional diffusion. ESAIM: M2AN, 53(4), 1245-1268 | en_US |
dc.identifier.uri | http://hdl.handle.net/10034/622682 | |
dc.description.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. | en_US |
dc.publisher | EDP Sciences | en_US |
dc.relation.url | https://www.esaim-m2an.org/articles/m2an/abs/2019/04/m2an180176/m2an180176.html | en_US |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/4.0/ | en_US |
dc.subject | stochastic time-fractional diffusion | en_US |
dc.subject | Galerkin finite element method | en_US |
dc.subject | strong convergence | en_US |
dc.subject | weak convergence | en_US |
dc.title | Numerical Approximation of Stochastic Time-Fractional Diffusion | en_US |
dc.type | Article | en_US |
dc.identifier.eissn | 1290-3841 | en_US |
dc.contributor.department | University of Chester; University College London; The Hong Kong Polytechnic University | en_US |
dc.identifier.journal | ESAIM: M2AN | en_US |
or.grant.openaccess | Yes | en_US |
rioxxterms.funder | unfunded research | en_US |
rioxxterms.identifier.project | unfunded research | en_US |
rioxxterms.version | AM | en_US |
rioxxterms.versionofrecord | 10.1051/m2an/2019025 | en_US |
rioxxterms.licenseref.startdate | 2019-07-09 | |
rioxxterms.publicationdate | 2019-07-09 | |
dc.dateAccepted | 2019-03-16 | |
dc.date.deposited | 2019-10-08 | en_US |
dc.indentifier.issn | 0764-583X | en_US |