Exponential convergence of hp-FEM for the integral fractional Laplacian in 1D
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866911965222273024 |
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| author | Faustmann, Markus Marcati, Carlo Melenk, Jens Markus Schwab, Christoph |
| author_facet | Faustmann, Markus Marcati, Carlo Melenk, Jens Markus Schwab, Christoph |
| contents | We prove weighted analytic regularity for the solution of the integral fractional Poisson problem on bounded intervals with analytic right-hand side. Based on this regularity result, we prove exponential convergence of the hp-FEM on geometric boundary-refined meshes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2204_04113 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Exponential convergence of hp-FEM for the integral fractional Laplacian in 1D Faustmann, Markus Marcati, Carlo Melenk, Jens Markus Schwab, Christoph Numerical Analysis Analysis of PDEs We prove weighted analytic regularity for the solution of the integral fractional Poisson problem on bounded intervals with analytic right-hand side. Based on this regularity result, we prove exponential convergence of the hp-FEM on geometric boundary-refined meshes. |
| title | Exponential convergence of hp-FEM for the integral fractional Laplacian in 1D |
| topic | Numerical Analysis Analysis of PDEs |
| url | https://arxiv.org/abs/2204.04113 |