Mixed finite elements for incompressible magneto-hydrodynamics

Anna Schneebeli; Dominik Schötzau

doi:10.1016/S1631-073X(03)00256-5

Numerical Analysis

Mixed finite elements for incompressible magneto-hydrodynamics
[Méthode d'éléments finis mixtes pour la magnéto-hydrodynamique incompressible]

Présenté par : Philippe G. Ciarlet

Anna Schneebeli ¹ ; Dominik Schötzau ¹

¹ Department of Mathematics, University of Basel, Rheinsprung 21, CH-4051 Switzerland

Comptes Rendus. Mathématique, Volume 337 (2003) no. 1, pp. 71-74.

Résumé
Abstract

Nous présentons une nouvelle méthode d'éléments finis mixtes pour les équations stationnaires tridimensionnelles de la magnéto-hydrodynamique incompressible. La partie fluide est discrétisée par des couples d'espaces standards vitesse–pression, stables selon la condition inf–sup, et la partie magnétique par une approche mixte utilisant les éléments de Nédélec de première espèce. Nous montrons que la méthode qui en résulte converge de façon quasi-optimale.

We present a new mixed finite element discretization for three-dimensional stationary incompressible magneto-hydrodynamics. The fluid variables are discretized by standard inf–sup stable velocity–pressure pairs and the magnetic variables by a mixed approach using Nédélec's elements of the first kind. The resulting method is shown to be quasi-optimally convergent.

Reçu le : 2003-04-04
Accepté le : 2003-05-16
Publié le : 2003-06-19

DOI : 10.1016/S1631-073X(03)00256-5

Affiliations des auteurs :

Anna Schneebeli ¹ ; Dominik Schötzau ¹

¹ Department of Mathematics, University of Basel, Rheinsprung 21, CH-4051 Switzerland

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     title = {Mixed finite elements for incompressible magneto-hydrodynamics},
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Anna Schneebeli; Dominik Schötzau. Mixed finite elements for incompressible magneto-hydrodynamics. Comptes Rendus. Mathématique, Volume 337 (2003) no. 1, pp. 71-74. doi : 10.1016/S1631-073X(03)00256-5. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(03)00256-5/

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