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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2018
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/1808.07825 |
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| _version_ | 1866911965190815744 |
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| author | Bernkopf, Maximilian Melenk, Jens Markus |
| author_facet | Bernkopf, Maximilian Melenk, Jens Markus |
| contents | Extending the wavenumber-explicit analysis of [Chen & Qiu, J. Comput. Appl. Math. 309 (2017)], we analyze the $L^2$-convergence of a least squares method for the Helmholtz equation with wavenumber $k$. For domains with an analytic boundary, we obtain improved rates in the mesh size $h$ and the polynomial degree $p$ under the scale resolution condition that $hk/p$ is sufficiently small and $p/\log k$ is sufficiently large. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1808_07825 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Analysis of the $hp$-version of a first order system least squares method for the Helmholtz equation Bernkopf, Maximilian Melenk, Jens Markus Numerical Analysis Extending the wavenumber-explicit analysis of [Chen & Qiu, J. Comput. Appl. Math. 309 (2017)], we analyze the $L^2$-convergence of a least squares method for the Helmholtz equation with wavenumber $k$. For domains with an analytic boundary, we obtain improved rates in the mesh size $h$ and the polynomial degree $p$ under the scale resolution condition that $hk/p$ is sufficiently small and $p/\log k$ is sufficiently large. |
| title | Analysis of the $hp$-version of a first order system least squares method for the Helmholtz equation |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/1808.07825 |