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Comptes Rendus Mathématique
Volume 337, n° 1
pages 71-74 (juillet 2003)
Doi : 10.1016/S1631-073X(03)00256-5
Received : 4 April 2003 ;  accepted : 16 May 2003
Mixed finite elements for incompressible magneto-hydrodynamics

Anna  Schneebeli,  Dominik  Schötzau
Department of Mathematics, University of Basel, Rheinsprung 21, CH-4051 Switzerland 

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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. To cite this article: A. Schneebeli, D. Schötzau, C. R. Acad. Sci. Paris, Ser. I 337 (2003).

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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. Pour citer cet article : A. Schneebeli, D. Schötzau, C. R. Acad. Sci. Paris, Ser. I 337 (2003).




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