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Nonconforming Finite Element Method for the Transmission Eigenvalue Problem

Part of:Ordinary differential operatorsPartial differential equations, initial value and time-dependent initial-boundary value problems

Published online by Cambridge University Press:  11 October 2016

Xia Ji,
Yingxia Xi and
Hehu Xie
Xia Ji*
Affiliation:
LSEC, NCMIS, Institute of Computational Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
Yingxia Xi*
Affiliation:
LSEC, NCMIS, Institute of Computational Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
Hehu Xie*
Affiliation:
LSEC, NCMIS, Institute of Computational Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
*
*Corresponding author. Email:jixia@lsec.cc.ac.cn (X. Ji), yxiaxi@lsec.cc.ac.cn (Y. Xi), hhxie@lsec.cc.ac.cn (H. Xie)
*Corresponding author. Email:jixia@lsec.cc.ac.cn (X. Ji), yxiaxi@lsec.cc.ac.cn (Y. Xi), hhxie@lsec.cc.ac.cn (H. Xie)
*Corresponding author. Email:jixia@lsec.cc.ac.cn (X. Ji), yxiaxi@lsec.cc.ac.cn (Y. Xi), hhxie@lsec.cc.ac.cn (H. Xie)

Abstract

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In this paper, we analyze a nonconforming finite element method for the computation of transmission eigenvalues and the corresponding eigenfunctions. The error estimates of the eigenvalue and eigenfunction approximation are given, respectively. Finally, some numerical examples are provided to validate the theoretical results.

Keywords

Transmission eigenvalueMorley elementnonconforming finite element method

MSC classification

Secondary:34L16: Numerical approximation of eigenvalues and of other parts of the spectrum65M60: Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods

Information

Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 9 , Issue 1 , February 2017, pp. 92 - 103
Copyright
Copyright © Global-Science Press 2017 

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