[La méthode de Galerkine discontinue symétrique est stable en une dimension d'espace pour tout ordre polynômial ]
Dans cette Note, nous montrons qu'en une dimension d'espace, la méthode de Galerkine discontinue symétrique pour les problèmes elliptiques d'ordre deux est stable pour tout ordre polynômial sans devoir introduire de paramètre de stabilisation. La méthode fournit des ordres de convergence optimaux dans la norme d'énergie (norme du gradient brisé plus des termes de saut) et dans la norme et peut être écrite sous forme conservative avec des flux indépendants de tout paramètre de stabilisation.
In this Note we prove that in one space dimension, the symmetric discontinuous Galerkin method for second order elliptic problems is stable for polynomial orders without using any stabilization parameter. The method yields optimal convergence rates in both the energy norm (-norm of broken gradient plus jump terms) and the -norm and can be written in conservative form with fluxes independent of any stabilization parameter.
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@article{CRMATH_2007__345_10_599_0,
author = {Burman, Erik and Ern, Alexandre and Mozolevski, Igor and Stamm, Benjamin},
title = {The symmetric discontinuous {Galerkin} method does not need stabilization in {1D} for polynomial orders $ p\ensuremath{\geqslant}2$},
journal = {Comptes Rendus. Math\'ematique},
pages = {599--602},
publisher = {Elsevier},
volume = {345},
number = {10},
year = {2007},
doi = {10.1016/j.crma.2007.10.028},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2007.10.028/}
}
TY - JOUR AU - Burman, Erik AU - Ern, Alexandre AU - Mozolevski, Igor AU - Stamm, Benjamin TI - The symmetric discontinuous Galerkin method does not need stabilization in 1D for polynomial orders $ p⩾2$ JO - Comptes Rendus. Mathématique PY - 2007 SP - 599 EP - 602 VL - 345 IS - 10 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2007.10.028/ DO - 10.1016/j.crma.2007.10.028 LA - en ID - CRMATH_2007__345_10_599_0 ER -
%0 Journal Article %A Burman, Erik %A Ern, Alexandre %A Mozolevski, Igor %A Stamm, Benjamin %T The symmetric discontinuous Galerkin method does not need stabilization in 1D for polynomial orders $ p⩾2$ %J Comptes Rendus. Mathématique %D 2007 %P 599-602 %V 345 %N 10 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2007.10.028/ %R 10.1016/j.crma.2007.10.028 %G en %F CRMATH_2007__345_10_599_0
Burman, Erik; Ern, Alexandre; Mozolevski, Igor; Stamm, Benjamin. The symmetric discontinuous Galerkin method does not need stabilization in 1D for polynomial orders $ p⩾2$. Comptes Rendus. Mathématique, Tome 345 (2007) no. 10, pp. 599-602. doi : 10.1016/j.crma.2007.10.028. http://www.numdam.org/articles/10.1016/j.crma.2007.10.028/
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