Issue |
ESAIM: M2AN
Volume 58, Number 3, May-June 2024
|
|
---|---|---|
Page(s) | 1185 - 1200 | |
DOI | https://doi.org/10.1051/m2an/2024033 | |
Published online | 27 June 2024 |
Error estimates for a mixed finite element method for the Maxwell’s transmission eigenvalue problem
1
MSU-BIT-SMBU Joint Research Center of Applied Mathematics, Shenzhen MSU-BIT University, Shenzhen 518001, P.R. China
2
Department of Mathematics, Jinan University, Guangdong 510632, P.R. China
3
Department of Mathematical Sciences, Michigan Technology University, Houghton, USA
* Corresponding author: cuijintao@jnu.edu.cn
Received:
12
December
2023
Accepted:
30
April
2024
In this paper, we analyze a numerical method combining the Ciarlet-Raviart mixed finite element formulation and an iterative algorithm for the Maxwell’s transmission eigenvalue problem. The eigenvalue problem is first written as a nonlinear quad-curl eigenvalue problem. Then the real transmission eigenvalues are proved to be the roots of a non-linear function. They are the generalized eigenvalues of a related linear self-adjoint quad-curl eigenvalue problem. These generalized eigenvalues are computed by a mixed finite element method. We derive the error estimates using the spectral approximation of compact operators, the theory of mixed finite element method for quad-curl problems, and the derivatives of eigenvalues.
Mathematics Subject Classification: 65M60 / 65N30
Key words: Maxwell’s transmission eigenvalue / problem / mixed finite element method / error estimates
© The authors. Published by EDP Sciences, SMAI 2024
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