It is well known that the classical local projection
method as well as residual-based stabilization 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 a priori 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.