MIXED SPECTRAL ELEMENT APPROXIMATION OF THE NAVIER-STOKES EQUATIONS IN THE STREAM-FUNCTION AND VORTICITY-FORMULATION

This paper analyzes a new spectral element method to approximate the steady-state, incompressible Stokes and Navier-Stokes equations in a two-dimensional domain. It is based on the standard 'stream-function, vorticity' mixed formulation, discretized in each sub-domain by a spectral method, without or with numerical integration. The discrete spaces consist of continuous piecewise high-degree polynomial functions, to allow for an easy implementation of the algorithm. Except for the pressure, the error estimates are optimal.