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A Mixed Method for Maxwell Eigenproblem

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Abstract

We propose a mixed method for the computation of the eigenvalues of the Maxwell eigenproblem, in terms of the electric field and a multiplier. The method allows the Lagrange elements of any order greater than or equal to two for the electric field, while a piecewise constant element always for the multiplier. We show that optimal error estimates yield for singular as well as smooth solutions. For the Maxwell eigenproblem in L-shaped domain which has singular and smooth eigenfunctions, we present numerical results for illustrating the effectiveness of the proposed method and for confirming the theoretical results.

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Acknowledgements

The authors would like to thank the two anonymous referees very much for their very valuable comments and suggestions which have greatly helped us to improve the presentation of the paper. This work was partially supported by the National Natural Science Foundation of China under Grants 11971366, 11571266 and 11661161017, the Collaborative Innovation Centre of Mathematics, and the Hubei Key Laboratory of Computational Science (Wuhan University), and the Natural Science Foundation of Hubei Province No. 2019CFA007.

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Du, Z., Duan, H. A Mixed Method for Maxwell Eigenproblem. J Sci Comput 82, 8 (2020). https://doi.org/10.1007/s10915-019-01111-0

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