The least-squares pseudo-spectral method for Navier-Stokes equations

A spectral collocation approximation of first-order system least squares for incompressible Stokes equations was analyzed in Kim et al. (2004) [12], and finite element approximations for incompressible Navier-Stokes equations were developed in Bochev et al. (1998,1999) [9,10]. The aim of this paper is to analyze the first-order system least-squares pseudo-spectral method for incompressible Navier-Stokes equations. The paper will be an extension of the result in Kim et al. (2004) [12] to the Navier-Stokes equations. Our least-squares functional is defined by the sum of discrete spectral norms of a first-order system of equations corresponding to the Navier-Stokes equations based on Legendre-Gauss-Lobatto points. We show its ellipticity and continuity over an appropriate product space, and spectral convergences of discretization errors are derived in the H-1-norm and the L-2-norm in each variable. Finally, we present some numerical examples. (C) 2013 Elsevier Ltd. All rights reserved.