Document Type
Article
Publication Date
5-2024
Department
Department of Mathematical Sciences
Abstract
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.
Publication Title
ESAIM: Mathematical Modelling and Numerical Analysis
Recommended Citation
Wang, C.,
Cui, J.,
&
Sun, J.
(2024).
Error estimates for a mixed finite element method for the Maxwell's transmission eigenvalue problem.
ESAIM: Mathematical Modelling and Numerical Analysis,
58(3), 1185-1200.
http://doi.org/10.1051/m2an/2024033
Retrieved from: https://digitalcommons.mtu.edu/michigantech-p2/938
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.
Version
Publisher's PDF
Publisher's Statement
© The authors. Published by EDP Sciences, SMAI 2024. Publisher’s version of record: https://doi.org/10.1051/m2an/2024033