FEM-BEM coupling for the high-frequency Helmholtz problem
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866913418477305856 |
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| author | Melenk, Jens Markus Perugia, Ilaria Rieder, Alexander |
| author_facet | Melenk, Jens Markus Perugia, Ilaria Rieder, Alexander |
| contents | We present a wavenumber-explicit analysis of FEM-BEM coupling methods for time-harmonic Helmholtz problems proposed in arXiv:2004.03523 for conforming discretizations and in arXiv:2105.06173 for discontinuous Galerkin (DG) volume discretizations. We show that the conditions that $kh/p$ be sufficiently small and that $\log(k) / p$ be bounded imply quasi-optimality of both conforming and DG-method, where $k$ is the wavenumber, $h$ the mesh size, and $p$ the approximation order. The analysis relies on a $k$-explicit regularity theory for a three-field coupling formulation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_04428 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | FEM-BEM coupling for the high-frequency Helmholtz problem Melenk, Jens Markus Perugia, Ilaria Rieder, Alexander Numerical Analysis 65N38, 65N30, 65N12 We present a wavenumber-explicit analysis of FEM-BEM coupling methods for time-harmonic Helmholtz problems proposed in arXiv:2004.03523 for conforming discretizations and in arXiv:2105.06173 for discontinuous Galerkin (DG) volume discretizations. We show that the conditions that $kh/p$ be sufficiently small and that $\log(k) / p$ be bounded imply quasi-optimality of both conforming and DG-method, where $k$ is the wavenumber, $h$ the mesh size, and $p$ the approximation order. The analysis relies on a $k$-explicit regularity theory for a three-field coupling formulation. |
| title | FEM-BEM coupling for the high-frequency Helmholtz problem |
| topic | Numerical Analysis 65N38, 65N30, 65N12 |
| url | https://arxiv.org/abs/2407.04428 |