C0 IP Methods for the Transmission Eigenvalue Problem

Hongrui Geng; Xia Ji; Jiguang Sun; Liwei Xu

doi:10.1007/s10915-015-0140-2

C⁰ IP Methods for the Transmission Eigenvalue Problem

Hongrui Geng, Xia Ji^*, Jiguang Sun, Liwei Xu

^*此作品的通讯作者

科研成果: 期刊稿件 › 文章 › 同行评审

31 引用（Scopus）

摘要

We consider a non-selfadjoint fourth order eigenvalue problem using a discontinuous Galerkin (DG) method. For high order problems, DG methods are competitive since they use simple basis functions and have less degrees of freedom. The numerical implementation is much easier compared with classical conforming finite element methods. In this paper, we propose an interior penalty discontinuous Galerkin method using C⁰ Lagrange elements (C⁰IP) for the transmission eigenvalue problem and prove the optimal convergence. The method is applied to several examples and its effectiveness is validated.

源语言	英语
页（从-至）	326-338
页数	13
期刊	Journal of Scientific Computing
卷	68
期	1
DOI	https://doi.org/10.1007/s10915-015-0140-2
出版状态	已出版 - 1 7月 2016
已对外发布	是

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Geng, H., Ji, X., Sun, J., & Xu, L. (2016). C⁰ IP Methods for the Transmission Eigenvalue Problem. Journal of Scientific Computing, 68(1), 326-338. https://doi.org/10.1007/s10915-015-0140-2

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title = "C0 IP Methods for the Transmission Eigenvalue Problem",

abstract = "We consider a non-selfadjoint fourth order eigenvalue problem using a discontinuous Galerkin (DG) method. For high order problems, DG methods are competitive since they use simple basis functions and have less degrees of freedom. The numerical implementation is much easier compared with classical conforming finite element methods. In this paper, we propose an interior penalty discontinuous Galerkin method using C0 Lagrange elements (C0IP) for the transmission eigenvalue problem and prove the optimal convergence. The method is applied to several examples and its effectiveness is validated.",

keywords = "Discontinuous Galerkin method, High order eigenvalue problem, Lagrange elements, Transmission eigenvalues",

author = "Hongrui Geng and Xia Ji and Jiguang Sun and Liwei Xu",

note = "Publisher Copyright: {\textcopyright} 2015, Springer Science+Business Media New York.",

year = "2016",

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doi = "10.1007/s10915-015-0140-2",

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T1 - C0 IP Methods for the Transmission Eigenvalue Problem

AU - Geng, Hongrui

AU - Ji, Xia

AU - Sun, Jiguang

AU - Xu, Liwei

PY - 2016/7/1

Y1 - 2016/7/1

N2 - We consider a non-selfadjoint fourth order eigenvalue problem using a discontinuous Galerkin (DG) method. For high order problems, DG methods are competitive since they use simple basis functions and have less degrees of freedom. The numerical implementation is much easier compared with classical conforming finite element methods. In this paper, we propose an interior penalty discontinuous Galerkin method using C0 Lagrange elements (C0IP) for the transmission eigenvalue problem and prove the optimal convergence. The method is applied to several examples and its effectiveness is validated.

AB - We consider a non-selfadjoint fourth order eigenvalue problem using a discontinuous Galerkin (DG) method. For high order problems, DG methods are competitive since they use simple basis functions and have less degrees of freedom. The numerical implementation is much easier compared with classical conforming finite element methods. In this paper, we propose an interior penalty discontinuous Galerkin method using C0 Lagrange elements (C0IP) for the transmission eigenvalue problem and prove the optimal convergence. The method is applied to several examples and its effectiveness is validated.

KW - Discontinuous Galerkin method

KW - High order eigenvalue problem

KW - Lagrange elements

KW - Transmission eigenvalues

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U2 - 10.1007/s10915-015-0140-2

DO - 10.1007/s10915-015-0140-2

M3 - Article

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SN - 0885-7474

VL - 68

SP - 326

EP - 338

JO - Journal of Scientific Computing

JF - Journal of Scientific Computing

IS - 1

ER -

C0 IP Methods for the Transmission Eigenvalue Problem

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C⁰ IP Methods for the Transmission Eigenvalue Problem