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A Multilevel Correction Method for Steklov Eigenvalue Problem by Nonconforming Finite Element Methods

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

Published online by Cambridge University Press:  05 August 2015

Xiaole Han ,
Yu Li  and
Hehu Xie
Xiaole Han
Affiliation:
Institute of Applied Physics and Computational Mathematics, Beijing 100094, China
Yu Li
Affiliation:
Research Center for Mathematics and Economics, Tianjin University of Finance and Economics, Tianjin 300222, China
Hehu Xie*
Affiliation:
LSEC, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
*
*Email addresses: hanxiaole@lsec.cc.ac.cn (X. Han), liyu@lsec.cc.ac.cn (Y. Li), hhxie@lsec.cc.ac.cn (H. Xie)
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Abstract

In this paper, a multilevel correction scheme is proposed to solve the Steklov eigenvalue problem by nonconforming finite element methods. With this new scheme, the accuracy of eigenpair approximations can be improved after each correction step which only needs to solve a source problem on finer finite element space and an Steklov eigenvalue problem on the coarsest finite element space. This correction scheme can increase the overall efficiency of solving eigenvalue problems by the nonconforming finite element method. Furthermore, as same as the direct eigenvalue solving by nonconforming finite element methods, this multilevel correction method can also produce the lower-bound approximations of the eigenvalues.

Keywords

Steklov eigenvalue problemmultilevel correctionnonconforming finite element 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
Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 8 , Issue 3 , August 2015 , pp. 383 - 405
Copyright
Copyright © Global-Science Press 2015 

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