Geodesic
A Superconvergence result for mixed finite element approximations of the eigenvalue problem
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 46 (2012) no. 4, pp. 797-812

Voir la notice de l'article provenant de la source Numdam

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 : 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 },
     pages = {797--812},
     publisher = {EDP-Sciences},
     volume = {46},
     number = {4},
     year = {2012},
     doi = {10.1051/m2an/2011065},
     mrnumber = {2891470},
     zbl = {1277.65091},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an/2011065/}
}
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 
PY  - 2012
SP  - 797
EP  - 812
VL  - 46
IS  - 4
PB  - EDP-Sciences
UR  - http://geodesic.mathdoc.fr/articles/10.1051/m2an/2011065/
DO  - 10.1051/m2an/2011065
LA  - en
ID  - M2AN_2012__46_4_797_0
ER  - 
%0 Journal Article
%A Lin, Qun
%A Xie, Hehu
%T A Superconvergence result for mixed finite element approximations of the eigenvalue problem
%J ESAIM: Mathematical Modelling and Numerical Analysis 
%D 2012
%P 797-812
%V 46
%N 4
%I EDP-Sciences
%U http://geodesic.mathdoc.fr/articles/10.1051/m2an/2011065/
%R 10.1051/m2an/2011065
%G en
%F 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 , Tome 46 (2012) no. 4, pp. 797-812. doi: 10.1051/m2an/2011065

Cité par Sources :