An exponentially convergent discretization for space-time fractional parabolic equations using $hp$-FEM
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866909265730469888 |
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| author | Melenk, Jens Markus Rieder, Alexander |
| author_facet | Melenk, Jens Markus Rieder, Alexander |
| contents | We consider a space-time fractional parabolic problem. Combining a sinc-quadrature based method for discretizing the Riesz-Dunford integral with $hp$-FEM in space yields an exponentially convergent scheme for the initial boundary value problem with homogeneous right-hand side. For the inhomogeneous problem, an $hp$-quadrature scheme is implemented. We rigorously prove exponential convergence with focus on small times $t$, proving robustness with respect to startup singularities due to data incompatibilities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2202_02067 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | An exponentially convergent discretization for space-time fractional parabolic equations using $hp$-FEM Melenk, Jens Markus Rieder, Alexander Numerical Analysis 65M60, 65M12, 65M15 We consider a space-time fractional parabolic problem. Combining a sinc-quadrature based method for discretizing the Riesz-Dunford integral with $hp$-FEM in space yields an exponentially convergent scheme for the initial boundary value problem with homogeneous right-hand side. For the inhomogeneous problem, an $hp$-quadrature scheme is implemented. We rigorously prove exponential convergence with focus on small times $t$, proving robustness with respect to startup singularities due to data incompatibilities. |
| title | An exponentially convergent discretization for space-time fractional parabolic equations using $hp$-FEM |
| topic | Numerical Analysis 65M60, 65M12, 65M15 |
| url | https://arxiv.org/abs/2202.02067 |