Wavenumber-explicit stability and convergence analysis of hp finite element discretizations of Helmholtz problems in piecewise smooth media
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2022
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| _version_ | 1866910314955538432 |
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| author | Bernkopf, M. Chaumont-Frelet, T. Melenk, J. M. |
| author_facet | Bernkopf, M. Chaumont-Frelet, T. Melenk, J. M. |
| contents | We present a wavenumber-explicit convergence analysis of the hp finite element method applied to a class of heterogeneous Helmholtz problems with piecewise analytic coefficients at large wavenumber $k$. Our analysis covers the heterogeneous Helmholtz equation with Robin, exact Dirichlet-to-Neumann, and second order absorbing boundary conditions, as well as perfectly matched layers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_03601 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Wavenumber-explicit stability and convergence analysis of hp finite element discretizations of Helmholtz problems in piecewise smooth media Bernkopf, M. Chaumont-Frelet, T. Melenk, J. M. Numerical Analysis Analysis of PDEs We present a wavenumber-explicit convergence analysis of the hp finite element method applied to a class of heterogeneous Helmholtz problems with piecewise analytic coefficients at large wavenumber $k$. Our analysis covers the heterogeneous Helmholtz equation with Robin, exact Dirichlet-to-Neumann, and second order absorbing boundary conditions, as well as perfectly matched layers. |
| title | Wavenumber-explicit stability and convergence analysis of hp finite element discretizations of Helmholtz problems in piecewise smooth media |
| topic | Numerical Analysis Analysis of PDEs |
| url | https://arxiv.org/abs/2209.03601 |