Two-level discretizations of the stream function form of the navier-stokes equations

In this report, we analyze a two level finite element method for the stream function formulation of the stationary Navier-stokes equation These methods were origionally proposed by Xu [12] and seem particularly well suited to the stream function form of the 2d Navier-stokes equation This report presents the algorithm and error analysis for the most basic case of conforming spaces two level discretizations and nonsingular solutions of (1.1).