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Volume 28, Issue 4
$H^2$-Conforming Methods and Two-Grid Discretizations for the Elastic Transmission Eigenvalue Problem

Yidu Yang, Jiayu Han & Hai Bi

DOI: 10.4208/cicp.OA-2019-0171

Commun. Comput. Phys., 28 (2020), pp. 1366-1388.

Published online: 2020-08

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  • Abstract

The elastic transmission eigenvalue problem has important applications in the inverse elastic scattering theory. Recently, the numerical computation for this problem has attracted the attention of the researchers. In this paper, we propose the $H^2$-conforming methods including the classical $H^2$-conforming finite element method and the spectral element method, and establish the two-grid discretization scheme. Theoretical analysis and numerical experiments show that the methods presented in this paper can efficiently compute real and complex elastic transmission eigenvalues.

  • Keywords

Elastic transmission eigenvalues, linear weak formulation, finite element, spectral element, the two-grid discretization, error estimates.

  • AMS Subject Headings

65N25, 65N30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-28-1366, author = {Yang , YiduHan , Jiayu and Bi , Hai}, title = {$H^2$-Conforming Methods and Two-Grid Discretizations for the Elastic Transmission Eigenvalue Problem}, journal = {Communications in Computational Physics}, year = {2020}, volume = {28}, number = {4}, pages = {1366--1388}, abstract = {

The elastic transmission eigenvalue problem has important applications in the inverse elastic scattering theory. Recently, the numerical computation for this problem has attracted the attention of the researchers. In this paper, we propose the $H^2$-conforming methods including the classical $H^2$-conforming finite element method and the spectral element method, and establish the two-grid discretization scheme. Theoretical analysis and numerical experiments show that the methods presented in this paper can efficiently compute real and complex elastic transmission eigenvalues.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2019-0171}, url = {http://global-sci.org/intro/article_detail/cicp/18103.html} }
TY - JOUR T1 - $H^2$-Conforming Methods and Two-Grid Discretizations for the Elastic Transmission Eigenvalue Problem AU - Yang , Yidu AU - Han , Jiayu AU - Bi , Hai JO - Communications in Computational Physics VL - 4 SP - 1366 EP - 1388 PY - 2020 DA - 2020/08 SN - 28 DO - http://doi.org/10.4208/cicp.OA-2019-0171 UR - https://global-sci.org/intro/article_detail/cicp/18103.html KW - Elastic transmission eigenvalues, linear weak formulation, finite element, spectral element, the two-grid discretization, error estimates. AB -

The elastic transmission eigenvalue problem has important applications in the inverse elastic scattering theory. Recently, the numerical computation for this problem has attracted the attention of the researchers. In this paper, we propose the $H^2$-conforming methods including the classical $H^2$-conforming finite element method and the spectral element method, and establish the two-grid discretization scheme. Theoretical analysis and numerical experiments show that the methods presented in this paper can efficiently compute real and complex elastic transmission eigenvalues.

Yang , YiduHan , Jiayu and Bi , Hai. (2020). $H^2$-Conforming Methods and Two-Grid Discretizations for the Elastic Transmission Eigenvalue Problem. Communications in Computational Physics. 28 (4). 1366-1388. doi:10.4208/cicp.OA-2019-0171
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