Comptes Rendus
Numerical Analysis
Mixed finite elements for incompressible magneto-hydrodynamics
[Méthode d'éléments finis mixtes pour la magnéto-hydrodynamique incompressible]
Comptes Rendus. Mathématique, Volume 337 (2003) no. 1, pp. 71-74.

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

Anna Schneebeli 1 ; Dominik Schötzau 1

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

[1] F. Armero; J.C. Simo Long-term dissipativity of time-stepping algorithms for an abstract evolution equation with applications to the incompressible MHD and Navier–Stokes equations, Comput. Methods Appl. Mech. Engrg., Volume 131 (1996), pp. 41-90

[2] M. Costabel; M. Dauge Weighted regularization of Maxwell equations in polyhedral domains, Numer. Math., Volume 93 (2002), pp. 239-277

[3] L. Demkowicz; L. Vardapetyan Modeling of electromagnetic absorption/scattering problems using hp-adaptive finite elements, Comput. Methods Appl. Mech. Engrg., Volume 152 (1998), pp. 103-124

[4] J.-F. Gerbeau A stabilized finite element method for the incompressible magnetohydrodynamic equations, Numer. Math., Volume 87 (2000), pp. 83-111

[5] J.-L. Guermond; P. Minev Mixed finite element approximation of an MHD problem involving conducting and insulating regions: the 2D case, Math. Model. Numer. Anal., Volume 36 (2002), pp. 517-536

[6] J.-L. Guermond, P. Minev, Mixed finite element approximation of an MHD problem involving conducting and insulating regions: the 3D case, Numer. Methods Partial Differential Equations, to appear

[7] M.D. Gunzburger; A.J. Meir; J.S. Peterson On the existence and uniqueness and finite element approximation of solutions of the equations of stationary incompressible magnetohydrodynamics, Math. Comp., Volume 56 (1991), pp. 523-563

[8] J.C. Nédélec Mixed finite elements in 3 , Numer. Math., Volume 35 (1980), pp. 315-341

[9] D. Schötzau, Mixed finite element methods for stationary incompressible magneto-hydrodynamics, Tech. report 2003-03, Department of Mathematics, University of Basel

[10] R. Hartmann, W. Bangerth, G. Kanschat, deal.II differential equations analysis library, technical reference, IWR, Universität Heidelberg, http://www.dealii.org

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