A spectral element method for the Navier-Stokes equations with improved accuracy

We present a procedure to enhance the accuracy of spectral element methods for the evolutionary Navier-Stokes equations. The approximations to the vel ocity and the pressure obtained using a spectral element method are postpro cessed by solving a discrete Stokes problem only once, when the time evolut ion is completed. The analysis shows that this procedure improves the order of convergence for the approximations to the velocity and the pressure. Th e choice of a discrete pressure space endowed with an inf-sup condition ind ependent of the discretization parameter leads to optimal error bounds for the pressure.