A Superconvergence result for mixed finite element approximations of the eigenvalue problem
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 46 (2012) no. 4, p. 797-812

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.

DOI : https://doi.org/10.1051/m2an/2011065
Classification:  65N30,  65N25,  65L15,  65B99
Keywords: second order elliptic eigenvalue problem, mixed finite element method, superconvergence
@article{M2AN_2012__46_4_797_0,
author = {Lin, Qun and Xie, Hehu},
title = {A Superconvergence result for mixed finite element approximations of the eigenvalue problem},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
publisher = {EDP-Sciences},
volume = {46},
number = {4},
year = {2012},
pages = {797-812},
doi = {10.1051/m2an/2011065},
zbl = {1277.65091},
mrnumber = {2891470},
language = {en},
url = {http://www.numdam.org/item/M2AN_2012__46_4_797_0}
}

Lin, Qun; Xie, Hehu. A Superconvergence result for mixed finite element approximations of the eigenvalue problem. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 46 (2012) no. 4, pp. 797-812. doi : 10.1051/m2an/2011065. http://www.numdam.org/item/M2AN_2012__46_4_797_0/

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