Wave number-Explicit Analysis for Galerkin Discretizations of Lossy Helmholtz Problems
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arXiv
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| Format: | Preprint |
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2019
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| _version_ | 1866917731317579776 |
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| author | Melenk, Jens M. Sauter, Stefan A. Torres, Céline |
| author_facet | Melenk, Jens M. Sauter, Stefan A. Torres, Céline |
| contents | We present a stability and convergence theory for the lossy Helmholtz equation and its Galerkin discretization. The boundary conditions are of Robin type. All estimates are explicit with respect to the real and imaginary part of the complex wave number $ζ\in\mathbb{C}$, $\operatorname{Re}ζ\geq0$, $\left\vert ζ\right\vert \geq1$. For the extreme cases $ζ\in\operatorname*{i}\mathbb{R}$ and $ζ\in\mathbb{R}_{\geq0}$, the estimates coincide with the existing estimates in the literature and exhibit a seamless transition between these cases in the right complex half plane. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1904_00207 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Wave number-Explicit Analysis for Galerkin Discretizations of Lossy Helmholtz Problems Melenk, Jens M. Sauter, Stefan A. Torres, Céline Numerical Analysis We present a stability and convergence theory for the lossy Helmholtz equation and its Galerkin discretization. The boundary conditions are of Robin type. All estimates are explicit with respect to the real and imaginary part of the complex wave number $ζ\in\mathbb{C}$, $\operatorname{Re}ζ\geq0$, $\left\vert ζ\right\vert \geq1$. For the extreme cases $ζ\in\operatorname*{i}\mathbb{R}$ and $ζ\in\mathbb{R}_{\geq0}$, the estimates coincide with the existing estimates in the literature and exhibit a seamless transition between these cases in the right complex half plane. |
| title | Wave number-Explicit Analysis for Galerkin Discretizations of Lossy Helmholtz Problems |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/1904.00207 |