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Volume 21, Issue 6
A High Order Unfitted Finite Element Method for Time-Harmonic Maxwell Interface Problems

Zhiming Chen, Ke Li, Maohui Lyu & Xueshaung Xiang

DOI: 10.4208/ijnam2024-1033

Int. J. Numer. Anal. Mod., 21 (2024), pp. 822-849.

Published online: 2024-10

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  • Abstract

We propose a high order unfitted finite element method for solving time-harmonic 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.

  • Keywords

Maxwell interface problem, high order unfitted finite element method, $hp$ a priori error estimate.

  • AMS Subject Headings

65N30, 35Q60

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{IJNAM-21-822, author = {Chen , ZhimingLi , KeLyu , Maohui and Xiang , Xueshaung}, title = {A High Order Unfitted Finite Element Method for Time-Harmonic Maxwell Interface Problems}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2024}, volume = {21}, number = {6}, pages = {822--849}, abstract = {

We propose a high order unfitted finite element method for solving time-harmonic 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.

}, issn = {2617-8710}, doi = {https://doi.org/10.4208/ijnam2024-1033}, url = {http://global-sci.org/intro/article_detail/ijnam/23462.html} }
TY - JOUR T1 - A High Order Unfitted Finite Element Method for Time-Harmonic Maxwell Interface Problems AU - Chen , Zhiming AU - Li , Ke AU - Lyu , Maohui AU - Xiang , Xueshaung JO - International Journal of Numerical Analysis and Modeling VL - 6 SP - 822 EP - 849 PY - 2024 DA - 2024/10 SN - 21 DO - http://doi.org/10.4208/ijnam2024-1033 UR - https://global-sci.org/intro/article_detail/ijnam/23462.html KW - Maxwell interface problem, high order unfitted finite element method, $hp$ a priori error estimate. AB -

We propose a high order unfitted finite element method for solving time-harmonic 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.

Zhiming Chen, Ke Li, Maohui Lyu & Xueshaung Xiang. (2024). A High Order Unfitted Finite Element Method for Time-Harmonic Maxwell Interface Problems. International Journal of Numerical Analysis and Modeling. 21 (6). 822-849. doi:10.4208/ijnam2024-1033
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