  The paper considers grad-div stabilized equal-order finite elements (FE)
methods for the linearized Navier-Stokes equations. A block triangular
preconditioner for the resulting system of algebraic equations is proposed
which is closely related to the Augmented Lagrangian (AL) preconditioner. A
field-of-values analysis of a preconditioned Krylov subspace method shows
convergence bounds that are independent of the mesh parameter variation.
Numerical studies support the theory and demonstrate the robustness of the
approach also with respect to the viscosity parameter variation, as is typical
for AL preconditioners when applied to inf-sup stable FE pairs. The numerical
experiments also address the accuracy of grad-div stabilized equal-order FE
method for the steady state Navier-Stokes equations.
