full
search.png

Search

close.png

Cancel

arrow
Volume 18, Issue 1
The Nonconforming Finite Element Methods for Two Transmission Eigenvalue Problems in Inverse Scattering

Lingling Sun, Hai Bi & Yidu Yang

DOI: 10.4208/aamm.OA-2023-0136

Adv. Appl. Math. Mech., 18 (2026), pp. 37-66.

Published online: 2025-10

Preview Full PDF 21 239

Cited by

google scholar semantic scholar
Export citation
  • Abstract

In this paper we study the nonconforming Crouzeix-Raviart element and the enriched Crouzeix-Raviart element methods firstly for the transmission eigenvalue problem of inhomogeneous media and the modified transmission eigenvalue problem in inverse scattering. Using $\mathbb{T}$-coercivity method, we prove the convergence and the a priori error estimate of approximate eigenpair for the transmission eigenvalue problem, and based on the obtained results we prove the a priori error estimate for the modified transmission eigenvalue problem by the $\mathbb{T}$-coercivity method and Gårding inequality, and further prove that the discrete eigenvalues for the problem with metamaterial background approximate the exact eigenvalue from above. We also carry out numerical experiments to validate the theoretical findings and the efficiency of the proposed methods.

  • Keywords

Transmission eigenvalue, modified transmission eigenvalue, nonconforming finite elements, error estimate, asymptotic upper bound.

  • AMS Subject Headings

65N25, 65N30

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{AAMM-18-37, author = {Sun , LinglingBi , Hai and Yang , Yidu}, title = {The Nonconforming Finite Element Methods for Two Transmission Eigenvalue Problems in Inverse Scattering}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2025}, volume = {18}, number = {1}, pages = {37--66}, abstract = {

In this paper we study the nonconforming Crouzeix-Raviart element and the enriched Crouzeix-Raviart element methods firstly for the transmission eigenvalue problem of inhomogeneous media and the modified transmission eigenvalue problem in inverse scattering. Using $\mathbb{T}$-coercivity method, we prove the convergence and the a priori error estimate of approximate eigenpair for the transmission eigenvalue problem, and based on the obtained results we prove the a priori error estimate for the modified transmission eigenvalue problem by the $\mathbb{T}$-coercivity method and Gårding inequality, and further prove that the discrete eigenvalues for the problem with metamaterial background approximate the exact eigenvalue from above. We also carry out numerical experiments to validate the theoretical findings and the efficiency of the proposed methods.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2023-0136}, url = {http://global-sci.org/intro/article_detail/aamm/24518.html} }
TY - JOUR T1 - The Nonconforming Finite Element Methods for Two Transmission Eigenvalue Problems in Inverse Scattering AU - Sun , Lingling AU - Bi , Hai AU - Yang , Yidu JO - Advances in Applied Mathematics and Mechanics VL - 1 SP - 37 EP - 66 PY - 2025 DA - 2025/10 SN - 18 DO - http://doi.org/10.4208/aamm.OA-2023-0136 UR - https://global-sci.org/intro/article_detail/aamm/24518.html KW - Transmission eigenvalue, modified transmission eigenvalue, nonconforming finite elements, error estimate, asymptotic upper bound. AB -

In this paper we study the nonconforming Crouzeix-Raviart element and the enriched Crouzeix-Raviart element methods firstly for the transmission eigenvalue problem of inhomogeneous media and the modified transmission eigenvalue problem in inverse scattering. Using $\mathbb{T}$-coercivity method, we prove the convergence and the a priori error estimate of approximate eigenpair for the transmission eigenvalue problem, and based on the obtained results we prove the a priori error estimate for the modified transmission eigenvalue problem by the $\mathbb{T}$-coercivity method and Gårding inequality, and further prove that the discrete eigenvalues for the problem with metamaterial background approximate the exact eigenvalue from above. We also carry out numerical experiments to validate the theoretical findings and the efficiency of the proposed methods.

Sun , LinglingBi , Hai and Yang , Yidu. (2025). The Nonconforming Finite Element Methods for Two Transmission Eigenvalue Problems in Inverse Scattering. Advances in Applied Mathematics and Mechanics. 18 (1). 37-66. doi:10.4208/aamm.OA-2023-0136
Copy to clipboard
BibteX RIS TXT
The citation has been copied to your clipboard