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It is well known that the classical local projection method as well as residual-based stabi- lization techniques, as for instance streamline upwind Petrov-Galerkin (SUPG), are optimal on isotropic meshes. Here we extend the local projection stabilization for the Navier-Stokes system to anisotropic quadrilateral meshes in two spatial dimensions. We describe the new method and prove an ap riori error estimate. This method leads on anisotropic meshes to qualitatively better convergence behavior than other isotropic stabilization methods. The capability of the method is illustrated by means of two numerical test problems. Mathematics Subject Classification. 35Q30, 65N30, 76D05.

A stabilized finite element scheme for the Navier-Stokes equations on quadrilateral anisotropic meshes