A finite element time relaxation method

Roland Becker; Erik Burman; Peter Hansbo

doi:10.1016/j.crma.2010.12.010

Numerical Analysis

A finite element time relaxation method

Présenté par : the Editorial Board

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

Comptes Rendus. Mathématique, Volume 349 (2011) no. 5-6, pp. 353-356.

Résumé
Abstract

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.

Reçu le : 2010-09-22
Accepté le : 2010-12-04
Publié le : 2011-02-18

DOI : 10.1016/j.crma.2010.12.010

Affiliations des auteurs :

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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     title = {A finite element time relaxation method},
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     pages = {353--356},
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     number = {5-6},
     year = {2011},
     doi = {10.1016/j.crma.2010.12.010},
     language = {en},
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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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