Efficient finite element numerical solution of the variable coefficient fractional subdiffusion equation
Abstract Based on the weighted and shifted Grünwald formula, a fully discrete finite element scheme is derived for the variable coefficient time-fractional subdiffusion equation. Firstly, the unconditional stable and convergent of the fully discrete scheme in L1(H1) $L^{1}(H^{1})$-norm is proved. Se...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2019-03-01
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| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13662-019-2048-x |
| _version_ | 1818042811279212544 |
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| author | Lin He Juncheng Lv |
| author_facet | Lin He Juncheng Lv |
| author_sort | Lin He |
| collection | DOAJ |
| description | Abstract Based on the weighted and shifted Grünwald formula, a fully discrete finite element scheme is derived for the variable coefficient time-fractional subdiffusion equation. Firstly, the unconditional stable and convergent of the fully discrete scheme in L1(H1) $L^{1}(H^{1})$-norm is proved. Secondly, through a new estimate approach, the superclose properties are obtained. The global superconvergence order O(τ2+hm+1) $\mathcal{O}(\tau ^{2}+h^{m+1})$ is deduced with the help of interpolation postprocessing technique. Finally, some numerical results are provided to verify the theoretical analysis. |
| first_indexed | 2024-12-10T08:52:15Z |
| format | Article |
| id | doaj.art-cd32ef13253d400596b913d4cbe85c9b |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-12-10T08:52:15Z |
| publishDate | 2019-03-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-cd32ef13253d400596b913d4cbe85c9b2022-12-22T01:55:33ZengSpringerOpenAdvances in Difference Equations1687-18472019-03-012019111710.1186/s13662-019-2048-xEfficient finite element numerical solution of the variable coefficient fractional subdiffusion equationLin He0Juncheng Lv1College of Information Engineering, Zhengzhou Institute of Finance and EconomicsHenan Geology Mineral CollegeAbstract Based on the weighted and shifted Grünwald formula, a fully discrete finite element scheme is derived for the variable coefficient time-fractional subdiffusion equation. Firstly, the unconditional stable and convergent of the fully discrete scheme in L1(H1) $L^{1}(H^{1})$-norm is proved. Secondly, through a new estimate approach, the superclose properties are obtained. The global superconvergence order O(τ2+hm+1) $\mathcal{O}(\tau ^{2}+h^{m+1})$ is deduced with the help of interpolation postprocessing technique. Finally, some numerical results are provided to verify the theoretical analysis.http://link.springer.com/article/10.1186/s13662-019-2048-xSubdiffusion equationWeighted and shifted Grünwald formulaFinite element methodSuperconvergence estimate |
| spellingShingle | Lin He Juncheng Lv Efficient finite element numerical solution of the variable coefficient fractional subdiffusion equation Advances in Difference Equations Subdiffusion equation Weighted and shifted Grünwald formula Finite element method Superconvergence estimate |
| title | Efficient finite element numerical solution of the variable coefficient fractional subdiffusion equation |
| title_full | Efficient finite element numerical solution of the variable coefficient fractional subdiffusion equation |
| title_fullStr | Efficient finite element numerical solution of the variable coefficient fractional subdiffusion equation |
| title_full_unstemmed | Efficient finite element numerical solution of the variable coefficient fractional subdiffusion equation |
| title_short | Efficient finite element numerical solution of the variable coefficient fractional subdiffusion equation |
| title_sort | efficient finite element numerical solution of the variable coefficient fractional subdiffusion equation |
| topic | Subdiffusion equation Weighted and shifted Grünwald formula Finite element method Superconvergence estimate |
| url | http://link.springer.com/article/10.1186/s13662-019-2048-x |
| work_keys_str_mv | AT linhe efficientfiniteelementnumericalsolutionofthevariablecoefficientfractionalsubdiffusionequation AT junchenglv efficientfiniteelementnumericalsolutionofthevariablecoefficientfractionalsubdiffusionequation |