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Computable Error Estimates for a Nonsymmetric Eigenvalue Problem

Part of: Numerical analysis: Ordinary differential equations Acceleration of convergence Partial differential equations, boundary value problems

Published online by Cambridge University Press:  07 September 2017

Hehu Xie ,
Manting Xie ,
Xiaobo Yin  and
Meiling Yue
Hehu Xie*
Affiliation:
LSEC, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China; and School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, 100049, China
Manting Xie*
Affiliation:
LSEC, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China; and School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, 100049, China
Xiaobo Yin*
Affiliation:
School of Mathematics and Statistics & Hubei Key Laboratory of Mathematical Sciences, Central China Normal University, Wuhan 430079, China
Meiling Yue*
Affiliation:
LSEC, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China; and School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, 100049, China
*
*Corresponding author. Email addresses:hhxie@lsec.cc.ac.cn (H. Xie), xiemanting@lsec.cc.ac.cn (M. Xie), yinxb@mail.ccnu.edu.cn (X. Yin), yuemeiling@lsec.cc.ac.cn (M. Yue)
*Corresponding author. Email addresses:hhxie@lsec.cc.ac.cn (H. Xie), xiemanting@lsec.cc.ac.cn (M. Xie), yinxb@mail.ccnu.edu.cn (X. Yin), yuemeiling@lsec.cc.ac.cn (M. Yue)
*Corresponding author. Email addresses:hhxie@lsec.cc.ac.cn (H. Xie), xiemanting@lsec.cc.ac.cn (M. Xie), yinxb@mail.ccnu.edu.cn (X. Yin), yuemeiling@lsec.cc.ac.cn (M. Yue)
*Corresponding author. Email addresses:hhxie@lsec.cc.ac.cn (H. Xie), xiemanting@lsec.cc.ac.cn (M. Xie), yinxb@mail.ccnu.edu.cn (X. Yin), yuemeiling@lsec.cc.ac.cn (M. Yue)

Abstract

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We provide some computable error estimates in solving a nonsymmetric eigenvalue problem by general conforming finite element methods on general meshes. Based on the complementary method, we first give computable error estimates for both the original eigenfunctions and the corresponding adjoint eigenfunctions, and then we introduce a generalised Rayleigh quotient to deduce a computable error estimate for the eigenvalue approximations. Some numerical examples are presented to illustrate our theoretical results.

Keywords

Nonsymmetric eigenvalue problemcomputable error estimatesasymptotical exactnessfinite element methodcomplementary method

MSC classification

Secondary: 65N30: Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods 65N25: Eigenvalue problems 65L15: Eigenvalue problems 65B99: None of the above, but in this section

Information

Type
Research Article
Information
East Asian Journal on Applied Mathematics , Volume 7 , Issue 3 , August 2017 , pp. 583 - 602
Copyright
Copyright © Global-Science Press 2017 

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