  We study the steady-state Navier-Stokes equations in the context of
stochastic finite element discretizations. Specifically, we assume that the
viscosity is a random field given in the form of a generalized polynomial chaos
expansion. For the resulting stochastic problem, we formulate the model and
linearization schemes using Picard and Newton iterations in the framework of
the stochastic Galerkin method, and we explore properties of the resulting
stochastic solutions. We also propose a preconditioner for solving the linear
systems of equations arising at each step of the stochastic (Galerkin)
nonlinear iteration and demonstrate its effectiveness for solving a set of
benchmark problems.
