Local and parallel finite element algorithms based on two-grid discretization for the stream function form of Navier-Stokes equations

A new local and parallel discretization finite element algorithms are proposed and analyzed in this paper for the stream function form of Navier-Stokes equations according to [1]. The theoretical tools for analyzing these methods are some local priori estimate that are also obtained in this paper for finite element solutions on general shape-regular grids. Some numerical experiments are also presented to support the theory.