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C0IPG for a Fourth Order Eigenvalue Problem

Part of: Partial differential equations, boundary value problems

Published online by Cambridge University Press:  01 February 2016

Xia Ji ,
Hongrui Geng ,
Jiguang Sun  and
Liwei Xu
Xia Ji*
Affiliation:
LSEC, Institute of Computational Mathematics, Chinese Academy of Sciences, Beijing 100190, P.R. China
Hongrui Geng
Affiliation:
College of Mathematics and Statistics, Chongqing University, Chongqing 401331, P.R. China
Jiguang Sun
Affiliation:
Department of Mathematical Sciences, Michigan Technological University, Houghton, MI 49931, United States
Liwei Xu
Affiliation:
College of Mathematics and Statistics, Chongqing University, Chongqing 401331, P.R. China Institute of Computing and Data Sciences, Chongqing University, Chongqing 400044, P.R. China
*
*Corresponding author. Email addresses:jixia@lsec.cc.ac.cn (X. Ji), ghr0313@hotmail.com (H. Geng), jiguangs@mtu.edu (J. Sun), xul@cqu.edu.cn (L. Xu)

Abstract

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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 (C0IPG) 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.

Keywords

Fourth order eigenvalue problemdiscontinuous Galerkin methodspectrum approximation

MSC classification

Secondary: 65N25: Eigenvalue problems 65N30: Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods 65N22: Solution of discretized equations

Information

Type
Research Article
Information
Communications in Computational Physics , Volume 19 , Issue 2 , February 2016 , pp. 393 - 410
Copyright
Copyright © Global-Science Press 2016 

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