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

- Volume: 46, Issue: 4, page 797-812
- ISSN: 0764-583X

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topLin, Qun, and 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 46.4 (2012): 797-812. <http://eudml.org/doc/273223>.

@article{Lin2012,

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.},

author = {Lin, Qun, Xie, Hehu},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},

keywords = {second order elliptic eigenvalue problem; mixed finite element method; superconvergence; second-order elliptic eigenvalue problem; eigenfunction approximation; lowest-order Raviart-Thomas approximation; numerical experiments},

language = {eng},

number = {4},

pages = {797-812},

publisher = {EDP-Sciences},

title = {A Superconvergence result for mixed finite element approximations of the eigenvalue problem},

url = {http://eudml.org/doc/273223},

volume = {46},

year = {2012},

}

TY - JOUR

AU - Lin, Qun

AU - Xie, Hehu

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

JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

PY - 2012

PB - EDP-Sciences

VL - 46

IS - 4

SP - 797

EP - 812

AB - 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.

LA - eng

KW - second order elliptic eigenvalue problem; mixed finite element method; superconvergence; second-order elliptic eigenvalue problem; eigenfunction approximation; lowest-order Raviart-Thomas approximation; numerical experiments

UR - http://eudml.org/doc/273223

ER -

## References

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