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dc.contributor.authorYan, Yubin
dc.contributor.authorJin, Bangti
dc.contributor.authorZhou, Zhi
dc.date.accessioned2019-10-08T08:55:26Z
dc.date.available2019-10-08T08:55:26Z
dc.date.issued2019-07-09
dc.identifier.citationJin, B., Yan, Y. & Zhou, Z. (2019). Numerical approximation of stochastic time-fractional diffusion. ESAIM: M2AN, 53(4), 1245-1268en_US
dc.identifier.urihttp://hdl.handle.net/10034/622682
dc.description.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.en_US
dc.publisherEDP Sciencesen_US
dc.relation.urlhttps://www.esaim-m2an.org/articles/m2an/abs/2019/04/m2an180176/m2an180176.htmlen_US
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/en_US
dc.subjectstochastic time-fractional diffusionen_US
dc.subjectGalerkin finite element methoden_US
dc.subjectstrong convergenceen_US
dc.subjectweak convergenceen_US
dc.titleNumerical Approximation of Stochastic Time-Fractional Diffusionen_US
dc.typeArticleen_US
dc.identifier.eissn1290-3841en_US
dc.contributor.departmentUniversity of Chester; University College London; The Hong Kong Polytechnic Universityen_US
dc.identifier.journalESAIM: M2ANen_US
or.grant.openaccessYesen_US
rioxxterms.funderunfunded researchen_US
rioxxterms.identifier.projectunfunded researchen_US
rioxxterms.versionAMen_US
rioxxterms.versionofrecord10.1051/m2an/2019025en_US
rioxxterms.licenseref.startdate2019-07-09
refterms.dateFCD2019-10-07T15:33:19Z
refterms.versionFCDAM
refterms.dateFOA2019-10-08T08:55:27Z
rioxxterms.publicationdate2019-07-09
dc.dateAccepted2019-03-16
dc.date.deposited2019-10-08en_US
dc.indentifier.issn0764-583Xen_US


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