An adaptive mesh refinement strategy to ensure quasi-optimality of finite element methods for self-adjoint Helmholtz problems
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916544035946496 |
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| author | van Beeck, Tim Zerbinati, Umberto |
| author_facet | van Beeck, Tim Zerbinati, Umberto |
| contents | It is well known that the quasi-optimality of the Galerkin finite element method for the Helmholtz equation is dependent on the mesh size and the wave-number. In the literature, different criteria have been proposed to ensure uniform quasi-optimality of the discretisation. In the present work, we study the uniform quasi-optimality of $H^1$ conforming and non-conforming Crouzeix-Raviart discretisation of the self-adjoint Helmholtz problem. In particular, we propose an adaptive scheme, coupled with a residual-based indicator, for generating guaranteed quasi-optimal meshes with minimal degrees of freedom. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_06266 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An adaptive mesh refinement strategy to ensure quasi-optimality of finite element methods for self-adjoint Helmholtz problems van Beeck, Tim Zerbinati, Umberto Numerical Analysis 65N30, 65N50, 65N15 It is well known that the quasi-optimality of the Galerkin finite element method for the Helmholtz equation is dependent on the mesh size and the wave-number. In the literature, different criteria have been proposed to ensure uniform quasi-optimality of the discretisation. In the present work, we study the uniform quasi-optimality of $H^1$ conforming and non-conforming Crouzeix-Raviart discretisation of the self-adjoint Helmholtz problem. In particular, we propose an adaptive scheme, coupled with a residual-based indicator, for generating guaranteed quasi-optimal meshes with minimal degrees of freedom. |
| title | An adaptive mesh refinement strategy to ensure quasi-optimality of finite element methods for self-adjoint Helmholtz problems |
| topic | Numerical Analysis 65N30, 65N50, 65N15 |
| url | https://arxiv.org/abs/2403.06266 |