, Volume 18, Issue 3, pp 255-291

Methodes d'elements finis mixtes pour les equations de stokes et de Navier-Stokes dans un polygone non convexe

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Abstract

We study a mixed finite element method for the steady-state Navier-Stokes equations in a polygon which is not necessarily convex. To take into account the signularities of the solution near the corners, we introduce weighted Sobolev spaces and prove the convergence of the method. The use of a non-uniformly regular family of triangulations allows us to get best error estimates.