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Extrapolation of Mixed Finite Element Approximations for the Maxwell Eigenvalue Problem

Published online by Cambridge University Press:  28 May 2015

Changhui Yao  and
Zhonghua Qiao
Changhui Yao*
Affiliation:
Department of Mathematics, Zhengzhou University, Zhengzhou, China
Zhonghua Qiao
Affiliation:
Institute for Computational Mathematics & Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong
*
Corresponding author.Email address:zqiao@math.hkbu.edu.hk
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Abstract

In this paper, a general method to derive asymptotic error expansion formulas for the mixed finite element approximations of the Maxwell eigenvalue problem is established. Abstract lemmas for the error of the eigenvalue approximations are obtained. Based on the asymptotic error expansion formulas, the Richardson extrapolation method is employed to improve the accuracy of the approximations for the eigenvalues of the Maxwell system from to when applying the lowest order Nédélec mixed finite element and a nonconforming mixed finite element. To our best knowledge, this is the first superconvergence result of the Maxwell eigenvalue problem by the extrapolation of the mixed finite element approximation. Numerical experiments are provided to demonstrate the theoretical results.

Keywords

65M1065N30Maxwell eigenvalue problemmixed finite elementasymptotic error expansionRichardson extrapolation

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Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 4 , Issue 3 , August 2011 , pp. 379 - 395
Copyright
Copyright © Global Science Press Limited 2011

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