Negative norm least-squares methods for the velocity-vorticity-pressure Navier-Stokes equations

We develop and analyze a least squares finite element method for the steady state, incompressible Navier-Stokes equations, written as a first-order system involving vorticity as new dependent variable. In contrast to standard L-2 least-squares methods for this system, our approach utilizes discrete negative norms in the least-squares functional. This allows us to devise efficient preconditioners for the discrete equations, and to establish optimal error estimates under relaxed regularity assumptions. (C) 1999 John Wiley & Sons, Inc.