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Volume 38, Issue 3
A Penalty-Free or Penalty-Factor-Free DG Method with a Locally Reconstructed Curl Operator for the Maxwell Eigenproblem

Zhijie Du, Huoyuan Duan & Duowei Zhu

DOI: 10.4208/cicp.OA-2024-0151

Commun. Comput. Phys., 38 (2025), pp. 887-922.

Published online: 2025-08

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  • Abstract

A new discontinuous Galerkin (DG) method is proposed and analyzed for the Maxwell eigenproblem, featuring a local reconstruction of the curl operator in a discontinuous finite element space. The proposed method can be penalty-free or penalty-factor-free, depending on which discontinuous finite element space the curl operator is locally reconstructed in. The new DG method is recast into a saddle-point problem so that it can be analyzed from the Babuška-Osborn theory for the finite element approximation of the spectrum of the compact operator, and the convergence and the optimal error estimates are then obtained; the discrete eigenmodes are spurious-free and spectral-correct. We provide numerical results to illustrate the proposed method.

  • Keywords

Maxwell eigenproblem, discontinuous Galerkin finite element method, local reconstruction, curl operator, convergence, error estimates.

  • AMS Subject Headings

65N30

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{CiCP-38-887, author = {Du , ZhijieDuan , Huoyuan and Zhu , Duowei}, title = {A Penalty-Free or Penalty-Factor-Free DG Method with a Locally Reconstructed Curl Operator for the Maxwell Eigenproblem}, journal = {Communications in Computational Physics}, year = {2025}, volume = {38}, number = {3}, pages = {887--922}, abstract = {

A new discontinuous Galerkin (DG) method is proposed and analyzed for the Maxwell eigenproblem, featuring a local reconstruction of the curl operator in a discontinuous finite element space. The proposed method can be penalty-free or penalty-factor-free, depending on which discontinuous finite element space the curl operator is locally reconstructed in. The new DG method is recast into a saddle-point problem so that it can be analyzed from the Babuška-Osborn theory for the finite element approximation of the spectrum of the compact operator, and the convergence and the optimal error estimates are then obtained; the discrete eigenmodes are spurious-free and spectral-correct. We provide numerical results to illustrate the proposed method.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2024-0151}, url = {http://global-sci.org/intro/article_detail/cicp/24318.html} }
TY - JOUR T1 - A Penalty-Free or Penalty-Factor-Free DG Method with a Locally Reconstructed Curl Operator for the Maxwell Eigenproblem AU - Du , Zhijie AU - Duan , Huoyuan AU - Zhu , Duowei JO - Communications in Computational Physics VL - 3 SP - 887 EP - 922 PY - 2025 DA - 2025/08 SN - 38 DO - http://doi.org/10.4208/cicp.OA-2024-0151 UR - https://global-sci.org/intro/article_detail/cicp/24318.html KW - Maxwell eigenproblem, discontinuous Galerkin finite element method, local reconstruction, curl operator, convergence, error estimates. AB -

A new discontinuous Galerkin (DG) method is proposed and analyzed for the Maxwell eigenproblem, featuring a local reconstruction of the curl operator in a discontinuous finite element space. The proposed method can be penalty-free or penalty-factor-free, depending on which discontinuous finite element space the curl operator is locally reconstructed in. The new DG method is recast into a saddle-point problem so that it can be analyzed from the Babuška-Osborn theory for the finite element approximation of the spectrum of the compact operator, and the convergence and the optimal error estimates are then obtained; the discrete eigenmodes are spurious-free and spectral-correct. We provide numerical results to illustrate the proposed method.

Du , ZhijieDuan , Huoyuan and Zhu , Duowei. (2025). A Penalty-Free or Penalty-Factor-Free DG Method with a Locally Reconstructed Curl Operator for the Maxwell Eigenproblem. Communications in Computational Physics. 38 (3). 887-922. doi:10.4208/cicp.OA-2024-0151
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