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Volume 30, Issue 4
A Simple Low-Degree Optimal Finite Element Scheme for the Elastic Transmission Eigenvalue Problem

Yingxia Xi, Xia Ji & Shuo Zhang

DOI: 10.4208/cicp.OA-2020-0260

Commun. Comput. Phys., 30 (2021), pp. 1061-1082.

Published online: 2021-08

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  • Abstract

The paper presents a finite element scheme for the elastic transmission eigenvalue problem written as a fourth order eigenvalue problem. The scheme uses piecewise cubic polynomials and obtains optimal convergence rate. Compared with other low-degree and nonconforming finite element schemes, the scheme inherits the continuous bilinear form which does not need extra stabilizations and is thus simple to implement.

  • Keywords

Elastic transmission eigenvalue problem, nonconforming finite element method, high accuracy

  • AMS Subject Headings

31A30, 65N30, 47B07

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-30-1061, author = {Xi , YingxiaJi , Xia and Zhang , Shuo}, title = {A Simple Low-Degree Optimal Finite Element Scheme for the Elastic Transmission Eigenvalue Problem}, journal = {Communications in Computational Physics}, year = {2021}, volume = {30}, number = {4}, pages = {1061--1082}, abstract = {

The paper presents a finite element scheme for the elastic transmission eigenvalue problem written as a fourth order eigenvalue problem. The scheme uses piecewise cubic polynomials and obtains optimal convergence rate. Compared with other low-degree and nonconforming finite element schemes, the scheme inherits the continuous bilinear form which does not need extra stabilizations and is thus simple to implement.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2020-0260}, url = {http://global-sci.org/intro/article_detail/cicp/19394.html} }
TY - JOUR T1 - A Simple Low-Degree Optimal Finite Element Scheme for the Elastic Transmission Eigenvalue Problem AU - Xi , Yingxia AU - Ji , Xia AU - Zhang , Shuo JO - Communications in Computational Physics VL - 4 SP - 1061 EP - 1082 PY - 2021 DA - 2021/08 SN - 30 DO - http://doi.org/10.4208/cicp.OA-2020-0260 UR - https://global-sci.org/intro/article_detail/cicp/19394.html KW - Elastic transmission eigenvalue problem, nonconforming finite element method, high accuracy AB -

The paper presents a finite element scheme for the elastic transmission eigenvalue problem written as a fourth order eigenvalue problem. The scheme uses piecewise cubic polynomials and obtains optimal convergence rate. Compared with other low-degree and nonconforming finite element schemes, the scheme inherits the continuous bilinear form which does not need extra stabilizations and is thus simple to implement.

Xi , YingxiaJi , Xia and Zhang , Shuo. (2021). A Simple Low-Degree Optimal Finite Element Scheme for the Elastic Transmission Eigenvalue Problem. Communications in Computational Physics. 30 (4). 1061-1082. doi:10.4208/cicp.OA-2020-0260
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