Asymptotic error expansion and Richardson extrapolation of eigenvalue approximations for second order elliptic problems by the mixed finite element method

Authors:
Qun Lin;Hehu Xie
Affiliations:
LSEC, Institute of Computational Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China;LSEC, Institute of Computational Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
Venue:
Applied Numerical Mathematics
Year:
2009

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Abstract

The paper provides a general procedure or method to produce asymptotic error expansion for the eigenvalue approximations of second order elliptic problems by the mixed finite element method. We obtain a transform lemma for the error of the eigenvalue approximations. As an application of the transform lemma, the asymptotic error expansion of the eigenvalue approximations for the second order elliptic problem by the lowest order Raviart-Thomas mixed finite element method is given by means of integral identity technique. Based on such an error expansion, Richardson extrapolation technique is applied to improve the accuracy of the eigenvalue approximations.