Error estimates of a continuous Galerkin time stepping method for subdiffusion problem
Affiliation
Jimei University; University of ChesterPublication Date
2021-07-29
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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.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/s10915-021-01587-9Publisher
SpringerJournal
Journal of Scientific ComputingAdditional Links
https://link.springer.com/article/10.1007/s10915-021-01587-9Type
ArticleDescription
This version of the article has been accepted for publication, after peer review (when applicable) and is subject to Springer Nature’s AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: http://dx.doi.org/10.1007/s10915-021-01587-9ISSN
0885-7474EISSN
1573-7691ae974a485f413a2113503eed53cd6c53
10.1007/s10915-021-01587-9
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Except where otherwise noted, this item's license is described as https://creativecommons.org/licenses/by-nc-nd/4.0/