Convergence of Legendre Methods for Navier-Stokes Equations

Abstract

This paper is concerned with spectral type of methods using Legendre polynomials. Both Galerkin and collocation approximations for the Navier-Stokes equations are considered and their rates of convergence are obtained. As a consequence, it is shown that these methods achieve spectral accuracy if the solutions to the Navier-Stokes equations are smooth.