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A Superconvergence result for mixed finite element approximations of the eigenvalue problem∗

Published online by Cambridge University Press:  03 February 2012

Qun Lin  and
Hehu Xie
Qun Lin
Affiliation:
LSEC, Institute of Computational Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, P.R. China. linq@lsec.cc.ac.cn ; hhxie@lsec.cc.ac.cn
Hehu Xie
Affiliation:
LSEC, Institute of Computational Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, P.R. China. linq@lsec.cc.ac.cn ; hhxie@lsec.cc.ac.cn
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Abstract

In this paper, we present a superconvergence result for the mixed finite element approximations of general second order elliptic eigenvalue problems. It is known that a superconvergence result has been given by Durán et al. [Math. Models Methods Appl. Sci. 9 (1999) 1165–1178] and Gardini [ESAIM: M2AN 43 (2009) 853–865] for the lowest order Raviart-Thomas approximation of Laplace eigenvalue problems. In this work, we introduce a new way to derive the superconvergence of general second order elliptic eigenvalue problems by general mixed finite element methods which have the commuting diagram property. Some numerical experiments are given to confirm the theoretical analysis.

Keywords

Second order elliptic eigenvalue problemmixed finite element methodsuperconvergence

Information

Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 46 , Issue 4 , July 2012 , pp. 797 - 812
Copyright
© EDP Sciences, SMAI, 2012

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