Comptes Rendus
no. 5-6
Numerical Analysis
A finite element time relaxation method

Présenté par : the Editorial Board

Roland Becker1 ; Erik Burman2 ; Peter Hansbo3
1 LMAP and INRIA Bordeaux Sud-Ouest, Université de Pau, 64013 Pau cedex, France
2 Department of Mathematics, University of Sussex, BN1 9QH Brighton, UK
3 Department of Mathematical Sciences, Chalmers University of Technology, S-412 62 Göteborg, Sweden
Comptes Rendus. Mathématique, Volume 349 (2011) no. 5-6, pp. 353-356.

Nous présentons une méthode dʼéléments finis de type relaxation de temps pour les écoulements de fluides à grand nombre de Reynolds. Cette approche utilise des projections locales sur un espace de polynômes défini sur des macor-éléments pour chaque paire dʼéléments adjacents à une face intérieure du maillage. Nous démontrons la stabilité et la convergence. Nous donnons des résultats pour lʼéquation de convection–diffusion et les équations instationnaires dʼEuler. Cette note se termine par des résultats numériques.

We discuss a finite element time-relaxation method for high Reynolds number flows. The method uses local projections on polynomials defined on macroelements of each pair of two elements sharing a face. We prove that this method shares the optimal stability and convergence properties of the continuous interior penalty (CIP) method. We give the formulation both for the scalar convection–diffusion equation and the time-dependent incompressible Euler equations and the associated convergence results. This note finishes with some numerical illustrations.

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Accepté le :
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DOI : 10.1016/j.crma.2010.12.010
Roland Becker 1 ; Erik Burman 2 ; Peter Hansbo 3

1 LMAP and INRIA Bordeaux Sud-Ouest, Université de Pau, 64013 Pau cedex, France
2 Department of Mathematics, University of Sussex, BN1 9QH Brighton, UK
3 Department of Mathematical Sciences, Chalmers University of Technology, S-412 62 Göteborg, Sweden 
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Roland Becker; Erik Burman; Peter Hansbo. A finite element time relaxation method. Comptes Rendus. Mathématique, Volume 349 (2011) no. 5-6, pp. 353-356. doi : 10.1016/j.crma.2010.12.010. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2010.12.010/

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