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Mixed finite element method for the Stokes and Navier-Stokes equations in a nonconvex polxgon. (Méthodes d’éléments finis mixtes pour les équations de Stokes et de Navier-Stokes dans un polygone non convexe.) (French. English summary) Zbl 0475.76035
Summary: 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 singularities 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.

MSC:
76M10 Finite element methods applied to problems in fluid mechanics
76D05 Navier-Stokes equations for incompressible viscous fluids
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
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