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Comptes Rendus Mathématique
Volume 341, n° 12
pages 769-774 (décembre 2005)
Doi : 10.1016/j.crma.2005.10.005
Received : 21 April 2005 ;  accepted : 11 October 2005
Estimations dʼerreur a priori de la méthode de Lagrange-Galerkin pour les systèmes de type Kazhikhov-Smagulov
A priori error estimates of the Lagrange-Galerkin method for Kazhikhov-Smagulov type systems

Jocelyn Étienne 1 , Pierre Saramito
LMC-IMAG, BP 53, 38041 Grenoble cedex, France 


Les systèmes de type Kazhikhov-Smagulov correspondent aux équations de Navier-Stokes non-homogènes et incompressibles lorsque la densité obéit à une loi de diffusion, comme dans les mélanges de gaz de densités différentes. Nous proposons un algorithme pour ces systèmes qui sʼappuie sur la discrétisation en temps par un schéma dʼEuler rétrograde de la méthode des caractéristiques, et sur une méthode dʼélements finis mixtes   pour la discrétisation en espace dans  ,  , des densités-vitesses-pressions. Sous la contrainte   et  , avec  , nous donnons une estimation dʼerreur optimale   pour le pas de temps δt et le pas de maillage h . Pour citer cet article : J. Étienne, P. Saramito, C. R. Acad. Sci. Paris, Ser. I 341 (2005).

The full text of this article is available in PDF format.

Kazhikhov-Smagulov type systems are a subclass of non-homogeneous, incompressible Navier-Stokes equations where density is subject to diffusion, as in mixtures of gases of different densities. An algorithm is devised for these systems, the time discretization being based on a backward-Euler scheme together with the method of characteristics, and a mixed density-velocity-pressure   finite element method is used for the space discretization in  ,  . Under the constraint that   and  , with  , we give optimal error bounds   for the time step δt and the mesh size h . To cite this article: J. Étienne, P. Saramito, C. R. Acad. Sci. Paris, Ser. I 341 (2005).

The full text of this article is available in PDF format.
1  Adresse actuelle : DAMTP, University of Cambridge, Wilberforce Road, Cambridge CB3 0EZ, Grande-Bretagne.

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