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dc.contributor.authorYan, Yubin
dc.contributor.authorYan, Yuyuan
dc.contributor.authorLiang, Zongqi
dc.contributor.authorEgwu, Bernard
dc.date.accessioned2021-10-01T08:31:22Z
dc.date.available2021-10-01T08:31:22Z
dc.date.issued2021-07-29
dc.identifierhttps://chesterrep.openrepository.com/bitstream/handle/10034/626002/ErrorEstimatesOfAContinuousGal.pdf?sequence=5
dc.identifier.citationYan, Y., Egwu, B. A., Liang, Z., Yan, Y. (2021). Error estimates of a continuous Galerkin Time Stepping Method for subdiffusion problem. Journal of Scientific Computing, 88, 68. https://doi.org/10.1007/s10915-021-01587-9en_US
dc.identifier.issn0885-7474
dc.identifier.doi10.1007/s10915-021-01587-9
dc.identifier.urihttp://hdl.handle.net/10034/626002
dc.description.abstractA continuous Galerkin time stepping method is introduced and analyzed for subdiffusion problem in an abstract setting. The approximate solution will be sought as a continuous piecewise linear function in time $t$ and the test space is based on the discontinuous piecewise constant functions. We prove that the proposed time stepping method has the convergence order $O(\tau^{1+ \alpha}), \, \alpha \in (0, 1)$ for general sectorial elliptic operators for nonsmooth data by using the Laplace transform method, where $\tau$ is the time step size. This convergence order is higher than the convergence orders of the popular convolution quadrature methods (e.g., Lubich's convolution methods) and L-type methods (e.g., L1 method), which have only $O(\tau)$ convergence for the nonsmooth data. Numerical examples are given to verify the robustness of the time discretization schemes with respect to data regularity.en_US
dc.publisherSpringeren_US
dc.relation.urlhttps://link.springer.com/article/10.1007/s10915-021-01587-9en_US
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.subjectSubdiffusion problemen_US
dc.subjectcontinuous Galerkin time stepping methoden_US
dc.subjectLaplace transformen_US
dc.subjectCaputo fractional derivativeen_US
dc.titleError estimates of a continuous Galerkin time stepping method for subdiffusion problemen_US
dc.typeArticleen_US
dc.identifier.eissn1573-7691en_US
dc.contributor.departmentJimei University; University of Chesteren_US
dc.identifier.journalJournal of Scientific Computingen_US
or.grant.openaccessYesen_US
rioxxterms.funderunfundeden_US
rioxxterms.identifier.projectunfundeden_US
rioxxterms.versionVoRen_US
rioxxterms.versionofrecord10.1007/s10915-021-01587-9en_US
rioxxterms.licenseref.startdate2022-07-29
dcterms.dateAccepted2021-07-20
rioxxterms.publicationdate2021-07-29
dc.date.deposited2021-10-01en_US
dc.indentifier.issn0885-7474en_US


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