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Volume 19, Issue 2
$C^0$IPG for a Fourth Order Eigenvalue Problem

Xia Ji, Hongrui Geng, Jiguang Sun & Liwei Xu

DOI: 10.4208/cicp.131014.140715a

Commun. Comput. Phys., 19 (2016), pp. 393-410.

Published online: 2018-04

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  • Abstract

This paper concerns numerical computation of a fourth order eigenvalue problem. We first show the well-posedness of the source problem. An interior penalty discontinuous Galerkin method ($C^0$IPG) using Lagrange elements is proposed and its convergence is studied. The method is then used to compute the eigenvalues. We show that the method is spectrally correct and prove the optimal convergence. Numerical examples are presented to validate the theory.

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@Article{CiCP-19-393, author = {Xia Ji, Hongrui Geng, Jiguang Sun and Liwei Xu}, title = {$C^0$IPG for a Fourth Order Eigenvalue Problem}, journal = {Communications in Computational Physics}, year = {2018}, volume = {19}, number = {2}, pages = {393--410}, abstract = {

This paper concerns numerical computation of a fourth order eigenvalue problem. We first show the well-posedness of the source problem. An interior penalty discontinuous Galerkin method ($C^0$IPG) using Lagrange elements is proposed and its convergence is studied. The method is then used to compute the eigenvalues. We show that the method is spectrally correct and prove the optimal convergence. Numerical examples are presented to validate the theory.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.131014.140715a}, url = {http://global-sci.org/intro/article_detail/cicp/11094.html} }
TY - JOUR T1 - $C^0$IPG for a Fourth Order Eigenvalue Problem AU - Xia Ji, Hongrui Geng, Jiguang Sun & Liwei Xu JO - Communications in Computational Physics VL - 2 SP - 393 EP - 410 PY - 2018 DA - 2018/04 SN - 19 DO - http://doi.org/10.4208/cicp.131014.140715a UR - https://global-sci.org/intro/article_detail/cicp/11094.html KW - AB -

This paper concerns numerical computation of a fourth order eigenvalue problem. We first show the well-posedness of the source problem. An interior penalty discontinuous Galerkin method ($C^0$IPG) using Lagrange elements is proposed and its convergence is studied. The method is then used to compute the eigenvalues. We show that the method is spectrally correct and prove the optimal convergence. Numerical examples are presented to validate the theory.

Xia Ji, Hongrui Geng, Jiguang Sun and Liwei Xu. (2018). $C^0$IPG for a Fourth Order Eigenvalue Problem. Communications in Computational Physics. 19 (2). 393-410. doi:10.4208/cicp.131014.140715a
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