A hybridizable discontinuous Galerkin method for the indefinite time-harmonic Maxwell equations
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2019
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| _version_ | 1866909401445564416 |
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| author | Chen, Gang Wu, Haijun Xu, Liwei |
| author_facet | Chen, Gang Wu, Haijun Xu, Liwei |
| contents | In this paper, we aim to develop a hybridizable discontinuous Galerkin (HDG) method for the indefinite time-harmonic Maxwell equations with the perfectly conducting boundary in the three-dimensional space. First, we derive the wavenumber explicit regularity result, which plays an important role in the error analysis for the HDG method. Second, we prove a discrete inf-sup condition which holds for all positive mesh size $h$, for all wavenumber $k$, and for general domain $Ω$. Then, we establish the optimal order error estimates of the underlying HDG method with constant independent of the wavenumber. The theoretical results are confirmed by numerical experiments. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1903_04161 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | A hybridizable discontinuous Galerkin method for the indefinite time-harmonic Maxwell equations Chen, Gang Wu, Haijun Xu, Liwei Numerical Analysis In this paper, we aim to develop a hybridizable discontinuous Galerkin (HDG) method for the indefinite time-harmonic Maxwell equations with the perfectly conducting boundary in the three-dimensional space. First, we derive the wavenumber explicit regularity result, which plays an important role in the error analysis for the HDG method. Second, we prove a discrete inf-sup condition which holds for all positive mesh size $h$, for all wavenumber $k$, and for general domain $Ω$. Then, we establish the optimal order error estimates of the underlying HDG method with constant independent of the wavenumber. The theoretical results are confirmed by numerical experiments. |
| title | A hybridizable discontinuous Galerkin method for the indefinite time-harmonic Maxwell equations |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/1903.04161 |