Estimations d'erreur a priori de la méthode de Lagrange–Galerkin pour les systèmes de type Kazhikhov–Smagulov

Abstract

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 ( P k , P k , P k − 1 ) finite element method is used for the space discretization in R d , d = 2 , 3 . Under the constraint that k > d − 1 and Δ t = C h r , with r ∈ ] d , 2 k + 2 − d [ , we give optimal error bounds O ( Δ t + h k ) for the time step Δ t and the mesh size h. To cite this article: J. Étienne, P. Saramito, C. R. Acad. Sci. Paris, Ser. I 341 (2005).