[Une remarque concernant la super-approximation et lʼextrapolation de lʼélement fini de Han pour les équations de Stokes]
Nous présentons une analyse de la super-convergence de lʼespace dʼélément finis de Han pour les équations de Stokes. Il est démontré que la différence entre la solution discrète et lʼinterpolé naturel de la solution nʼest pas de lʼordre supérieur ( « supercloseness »). Basé sur notre analyse, nous proposons une modification de lʼopérateur dʼinterpolation qui possède cette propriété. Cela permet la construction dʼun schéma dʼextrapolation simple qui est de lʼordre trois.
We analyze the supercloseness properties of the nonconforming quadrilateral Han finite element for the Stokes equations. It is shown that the difference between the discrete solution and the natural interpolation of the continuous solution does not have the supercloseness property. Based on this analysis, we propose a modified interpolation operator which allows for such a result. It is then used to obtain a simple third-order extrapolation scheme.
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@article{CRMATH_2011__349_17-18_1017_0,
author = {Li, Mingxia and Becker, Roland and Mao, Shipeng},
title = {A remark on supercloseness and extrapolation of the quadrilateral {Han} element for the {Stokes} equations},
journal = {Comptes Rendus. Math\'ematique},
pages = {1017--1020},
publisher = {Elsevier},
volume = {349},
number = {17-18},
year = {2011},
doi = {10.1016/j.crma.2011.08.005},
language = {en},
url = {http://archive.numdam.org/articles/10.1016/j.crma.2011.08.005/}
}
TY - JOUR AU - Li, Mingxia AU - Becker, Roland AU - Mao, Shipeng TI - A remark on supercloseness and extrapolation of the quadrilateral Han element for the Stokes equations JO - Comptes Rendus. Mathématique PY - 2011 SP - 1017 EP - 1020 VL - 349 IS - 17-18 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2011.08.005/ DO - 10.1016/j.crma.2011.08.005 LA - en ID - CRMATH_2011__349_17-18_1017_0 ER -
%0 Journal Article %A Li, Mingxia %A Becker, Roland %A Mao, Shipeng %T A remark on supercloseness and extrapolation of the quadrilateral Han element for the Stokes equations %J Comptes Rendus. Mathématique %D 2011 %P 1017-1020 %V 349 %N 17-18 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.crma.2011.08.005/ %R 10.1016/j.crma.2011.08.005 %G en %F CRMATH_2011__349_17-18_1017_0
Li, Mingxia; Becker, Roland; Mao, Shipeng. A remark on supercloseness and extrapolation of the quadrilateral Han element for the Stokes equations. Comptes Rendus. Mathématique, Tome 349 (2011) no. 17-18, pp. 1017-1020. doi : 10.1016/j.crma.2011.08.005. http://archive.numdam.org/articles/10.1016/j.crma.2011.08.005/
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