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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
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 |
| Summary: | 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. |
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| ISSN: | 1687-1847 |