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.
Mots clés : 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://www.numdam.org/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://www.numdam.org/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://www.numdam.org/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. http://www.numdam.org/articles/10.1051/m2an/2011065/
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