[Méthode d'éléments finis mixtes pour la magnéto-hydrodynamique incompressible]
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.
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@article{CRMATH_2003__337_1_71_0,
author = {Schneebeli, Anna and Sch\"otzau, Dominik},
title = {Mixed finite elements for incompressible magneto-hydrodynamics},
journal = {Comptes Rendus. Math\'ematique},
pages = {71--74},
publisher = {Elsevier},
volume = {337},
number = {1},
year = {2003},
doi = {10.1016/S1631-073X(03)00256-5},
language = {en},
url = {http://archive.numdam.org/articles/10.1016/S1631-073X(03)00256-5/}
}
TY - JOUR AU - Schneebeli, Anna AU - Schötzau, Dominik TI - Mixed finite elements for incompressible magneto-hydrodynamics JO - Comptes Rendus. Mathématique PY - 2003 SP - 71 EP - 74 VL - 337 IS - 1 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/S1631-073X(03)00256-5/ DO - 10.1016/S1631-073X(03)00256-5 LA - en ID - CRMATH_2003__337_1_71_0 ER -
%0 Journal Article %A Schneebeli, Anna %A Schötzau, Dominik %T Mixed finite elements for incompressible magneto-hydrodynamics %J Comptes Rendus. Mathématique %D 2003 %P 71-74 %V 337 %N 1 %I Elsevier %U http://archive.numdam.org/articles/10.1016/S1631-073X(03)00256-5/ %R 10.1016/S1631-073X(03)00256-5 %G en %F CRMATH_2003__337_1_71_0
Schneebeli, Anna; Schötzau, Dominik. Mixed finite elements for incompressible magneto-hydrodynamics. Comptes Rendus. Mathématique, Tome 337 (2003) no. 1, pp. 71-74. doi : 10.1016/S1631-073X(03)00256-5. http://archive.numdam.org/articles/10.1016/S1631-073X(03)00256-5/
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