Error estimates of a continuous Galerkin time stepping method for subdiffusion problem
dc.contributor.author | Yan, Yubin | |
dc.contributor.author | Yan, Yuyuan | |
dc.contributor.author | Liang, Zongqi | |
dc.contributor.author | Egwu, Bernard | |
dc.date.accessioned | 2021-10-01T08:31:22Z | |
dc.date.available | 2021-10-01T08:31:22Z | |
dc.date.issued | 2021-07-29 | |
dc.identifier | https://chesterrep.openrepository.com/bitstream/handle/10034/626002/ErrorEstimatesOfAContinuousGal.pdf?sequence=5 | |
dc.identifier.citation | Yan, 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/s10915-021-01587-9 | en_US |
dc.identifier.issn | 0885-7474 | |
dc.identifier.doi | 10.1007/s10915-021-01587-9 | |
dc.identifier.uri | http://hdl.handle.net/10034/626002 | |
dc.description.abstract | A 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.publisher | Springer | en_US |
dc.relation.url | https://link.springer.com/article/10.1007/s10915-021-01587-9 | en_US |
dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
dc.subject | Subdiffusion problem | en_US |
dc.subject | continuous Galerkin time stepping method | en_US |
dc.subject | Laplace transform | en_US |
dc.subject | Caputo fractional derivative | en_US |
dc.title | Error estimates of a continuous Galerkin time stepping method for subdiffusion problem | en_US |
dc.type | Article | en_US |
dc.identifier.eissn | 1573-7691 | en_US |
dc.contributor.department | Jimei University; University of Chester | en_US |
dc.identifier.journal | Journal of Scientific Computing | en_US |
or.grant.openaccess | Yes | en_US |
rioxxterms.funder | unfunded | en_US |
rioxxterms.identifier.project | unfunded | en_US |
rioxxterms.version | VoR | en_US |
rioxxterms.versionofrecord | 10.1007/s10915-021-01587-9 | en_US |
rioxxterms.licenseref.startdate | 2022-07-29 | |
dcterms.dateAccepted | 2021-07-20 | |
rioxxterms.publicationdate | 2021-07-29 | |
dc.date.deposited | 2021-10-01 | en_US |
dc.indentifier.issn | 0885-7474 | en_US |