Numerical Analysis
Symmetric and non-symmetric discontinuous Galerkin methods stabilized using bubble enrichment
Comptes Rendus. Mathématique, Volume 346 (2008) no. 1-2, pp. 103-106.

In this Note we prove that in two and three space dimensions, the symmetric and non-symmetric discontinuous Galerkin methods for second order elliptic problems are stable when using piecewise linear elements enriched with quadratic bubbles without any penalization of the interelement jumps. The method yields optimal convergence rates in both the broken energy norm and, in the symmetric case, the L2-norm. Moreover the method can be written in conservative form with fluxes independent of any stabilization parameter.

Dans cette Note, nous montrons qu'en deux et trois dimensions d'espace, les méthodes de Galerkine discontinue symétrique ou non-symétrique pour les problèmes elliptiques d'ordre deux sont stable pour l'ordre polynomial p=1 sans devoir introduire de terme de stabilisation si l'espace est enrichi par des bulles quadratiques. La méthode fournit des ordres de convergence optimaux dans la norme d'énergie brisée et, pour la formulation symétrique, dans la norme L2 et peut être écrite sous forme conservative avec des flux indépendants de tout paramètre de stabilisation.

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DOI: 10.1016/j.crma.2007.11.016
Burman, Erik 1; Stamm, Benjamin 1

1 IACS/CMCS, station 8, École polytechnique fédérale de Lausanne, CH 1015, Lausanne, Switzerland
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Burman, Erik; Stamm, Benjamin. Symmetric and non-symmetric discontinuous Galerkin methods stabilized using bubble enrichment. Comptes Rendus. Mathématique, Volume 346 (2008) no. 1-2, pp. 103-106. doi : 10.1016/j.crma.2007.11.016. http://www.numdam.org/articles/10.1016/j.crma.2007.11.016/

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