$hp$-FEM for the fractional heat equation
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2019
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| _version_ | 1866910539249090560 |
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| author | Melenk, Jens Markus Rieder, Alexander |
| author_facet | Melenk, Jens Markus Rieder, Alexander |
| contents | We consider a time dependent problem generated by a nonlocal operator in space. Applying a discretization scheme based on $hp$-Finite Elements and a Caffarelli-Silvestre extension we obtain a semidiscrete semigroup. The discretization in time is carried out by using $hp$-Discontinuous Galerkin based timestepping. We prove exponential convergence for such a method in an abstract framework for the discretization in the original domain $Ω$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1901_01767 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | $hp$-FEM for the fractional heat equation Melenk, Jens Markus Rieder, Alexander Numerical Analysis 65M60, 65M12, 65M15 We consider a time dependent problem generated by a nonlocal operator in space. Applying a discretization scheme based on $hp$-Finite Elements and a Caffarelli-Silvestre extension we obtain a semidiscrete semigroup. The discretization in time is carried out by using $hp$-Discontinuous Galerkin based timestepping. We prove exponential convergence for such a method in an abstract framework for the discretization in the original domain $Ω$. |
| title | $hp$-FEM for the fractional heat equation |
| topic | Numerical Analysis 65M60, 65M12, 65M15 |
| url | https://arxiv.org/abs/1901.01767 |