A high order unfitted finite element method for time-Harmonic Maxwell interface problems
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866912083641106432 |
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| author | Chen, Zhiming Li, Ke Lyu, Maohui Xiang, Xueshuang |
| author_facet | Chen, Zhiming Li, Ke Lyu, Maohui Xiang, Xueshuang |
| contents | We propose a high order unfitted finite element method for solving timeharmonic Maxwell interface problems. The unfitted finite element method is based on a mixed formulation in the discontinuous Galerkin framework on a Cartesian mesh with possible hanging nodes. The $H^2$ regularity of the solution to Maxwell interface problems with $C^2$ interfaces in each subdomain is proved. Practical interface-resolving mesh conditions are introduced under which the hp inverse estimates on three-dimensional curved domains are proved. Stability and hp a priori error estimate of the unfitted finite element method are proved. Numerical results are included to illustrate the performance of the method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_08944 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A high order unfitted finite element method for time-Harmonic Maxwell interface problems Chen, Zhiming Li, Ke Lyu, Maohui Xiang, Xueshuang Numerical Analysis We propose a high order unfitted finite element method for solving timeharmonic Maxwell interface problems. The unfitted finite element method is based on a mixed formulation in the discontinuous Galerkin framework on a Cartesian mesh with possible hanging nodes. The $H^2$ regularity of the solution to Maxwell interface problems with $C^2$ interfaces in each subdomain is proved. Practical interface-resolving mesh conditions are introduced under which the hp inverse estimates on three-dimensional curved domains are proved. Stability and hp a priori error estimate of the unfitted finite element method are proved. Numerical results are included to illustrate the performance of the method. |
| title | A high order unfitted finite element method for time-Harmonic Maxwell interface problems |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2301.08944 |