  The following paper compares a consistent Newton-Raphson and fixed-point
iteration based solution strategy for a variational multiscale finite element
formulation for incompressible Navier-Stokes. The main contributions of this
work include a consistent linearization of the Navier-Stokes equations, which
provides an avenue for advanced algorithms that require origins in a consistent
method. We also present a comparison between formulations that differ only in
their linearization, but maintain all other equivalences. Using the variational
multiscale concept, we construct a stabilized formulation (that may be
considered an extension of the MINI element to nonlinear Navier-Stokes). We
then linearize the problem using fixed-point iteration and by deriving a
consistent tangent matrix for the update equation to obtain the solution via
Newton-Raphson iterations. We show that the consistent formulation converges in
fewer iterations, as expected, for several test problems. We also show that the
consistent formulation converges for problems for which fixed-point iteration
diverges. We present the results of both methods for problems of Reynold's
number up to 5000.
