Nonconforming Finite Element Method for the Transmission Eigenvalue Problem

Nonconforming Finite Element Method for the Transmission Eigenvalue Problem

Year:    2017

Author:    Xia Ji, Yingxia Xi, Hehu Xie

Advances in Applied Mathematics and Mechanics, Vol. 9 (2017), Iss. 1 : pp. 92–103

Abstract

In this paper, we analyze a nonconforming finite element method for the computation of transmission eigenvalues and the corresponding eigenfunctions. The error estimates of the eigenvalue and eigenfunction approximation are given, respectively. Finally, some numerical examples are provided to validate the theoretical results.

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/aamm.2015.m1295

Advances in Applied Mathematics and Mechanics, Vol. 9 (2017), Iss. 1 : pp. 92–103

Published online:    2017-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    12

Keywords:    Transmission eigenvalue Morley element nonconforming finite element method.

Author Details

Xia Ji

Yingxia Xi

Hehu Xie

  1. A Novel Spectral Approximation and Error Estimation for Transmission Eigenvalues in Spherical Domains

    An, Jing | Tan, Ting | Zhang, Zhimin

    Journal of Scientific Computing, Vol. 96 (2023), Iss. 2

    https://doi.org/10.1007/s10915-023-02261-y [Citations: 2]
  2. Lowest-degree robust finite element schemes for inhomogeneous bi-Laplace problems

    Dai, Bin | Zeng, Huilan | Zhang, Chen-Song | Zhang, Shuo

    Applied Numerical Mathematics, Vol. 203 (2024), Iss. P.235

    https://doi.org/10.1016/j.apnum.2024.05.010 [Citations: 0]
  3. Legendre spectral method and error estimates for Helmholtz transmission eigenvalues in a cylinder

    Tan, Ting | Cao, Waixiang

    IMA Journal of Numerical Analysis, Vol. (2024), Iss.

    https://doi.org/10.1093/imanum/drae041 [Citations: 0]
  4. Discontinuous Galerkin Method for the Interior Transmission Eigenvalue Problem in Inverse Scattering Theory

    Meng, Jian

    Journal of Scientific Computing, Vol. 96 (2023), Iss. 3

    https://doi.org/10.1007/s10915-023-02290-7 [Citations: 1]
  5. A mixed element scheme for the Helmholtz transmission eigenvalue problem for anisotropic media

    Liu, Qing | Li, Tiexiang | Zhang, Shuo

    Inverse Problems, Vol. 39 (2023), Iss. 5 P.055005

    https://doi.org/10.1088/1361-6420/acc7c1 [Citations: 1]
  6. A lowest-order virtual element method for the Helmholtz transmission eigenvalue problem

    Meng, Jian | Wang, Gang | Mei, Liquan

    Calcolo, Vol. 58 (2021), Iss. 1

    https://doi.org/10.1007/s10092-020-00391-5 [Citations: 5]
  7. Spectral approximation and error analysis for the transmission eigenvalue problem with an isotropic inhomogeneous medium

    Tan, Ting | Cao, Waixiang

    Journal of Computational and Applied Mathematics, Vol. 453 (2025), Iss. P.116163

    https://doi.org/10.1016/j.cam.2024.116163 [Citations: 0]
  8. A multi-level mixed element scheme of the two-dimensional Helmholtz transmission eigenvalue problem

    Xi, Yingxia | Ji, Xia | Zhang, Shuo

    IMA Journal of Numerical Analysis, Vol. 40 (2020), Iss. 1 P.686

    https://doi.org/10.1093/imanum/dry061 [Citations: 8]
  9. Spectral approximation based on a mixed scheme and its error estimates for transmission eigenvalue problems

    Tan, Ting | Cao, Waixiang | An, Jing

    Computers & Mathematics with Applications, Vol. 111 (2022), Iss. P.20

    https://doi.org/10.1016/j.camwa.2022.02.009 [Citations: 10]
  10. Convergence of a lowest-order finite element method for the transmission eigenvalue problem

    Camaño, Jessika | Rodríguez, Rodolfo | Venegas, Pablo

    Calcolo, Vol. 55 (2018), Iss. 3

    https://doi.org/10.1007/s10092-018-0276-1 [Citations: 17]
  11. Mixed virtual element method for the Helmholtz transmission eigenvalue problem on polytopal meshes

    Meng, Jian | Wang, Gang | Mei, Liquan

    IMA Journal of Numerical Analysis, Vol. 43 (2023), Iss. 3 P.1685

    https://doi.org/10.1093/imanum/drac019 [Citations: 5]
  12. A High Accuracy Nonconforming Finite Element Scheme for Helmholtz Transmission Eigenvalue Problem

    Xi, Yingxia | Ji, Xia | Zhang, Shuo

    Journal of Scientific Computing, Vol. 83 (2020), Iss. 3

    https://doi.org/10.1007/s10915-020-01247-4 [Citations: 5]