Analysis of Least Squares Methods for Velocity Flux-Pressure-Velocity
Form of the Navier-Stokes Equations
Pavel Bochev
Department of Mathematics
University of Texas at Arlington
Box 19408, Arlington TX 76013-0408
Abstract. We present error analysis of a finite element method for the
Navier-Stokes equations based on least squares variational principles. The
method is formulated for the first order velocity flux-pressure-velocity form
of the Navier-Stokes equations suggested recently by Cai, Manteuffel and
McCormick. It is based on minimization of L^2 norms of the equation residuals.
The main results are optimal H^1 error estimates for all regular branches of
solutions of the respective Euler-Lagrange equations.
Unlike some other first order forms of the Navier-Stokes equations, the new
form permits coer-civity estimates in H^1(Omega) norms for all unknowns even
for the velocity boundary condition. As a result, the new formulation can be
effciently used in the context of the multigrid methods.