A multiscale V-P discretization for flow problems

This paper gives a comprehensive numerical analysis of a multiscale method for equilibrium Navier Stokes equations. The method includes pressure regularization and eddy viscosity stabilizations both acting only on the finest scales. This method allows for equal order velocity-pressure spaces as well as the linear constant pair and the usual (Pk, Pk−1) pair. We show the method is optimal in a natural energy norm for all of these pairs of spaces, and provide guidance in choosing the regularization parameters.