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 least-squares methods for this system, our approach utilizes discrete negative norms in the least-squares functional. This allows to devise efficient preconditioners for the discrete equations, and to establish optimal error estimates under relaxed regularity assumptions. c © 1998 John Wiley & Sons, Inc.

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