Newton's method for the Navier-Stokes equations with finite-element initial guess of stokes equations *

It is shown that finite element solutions of Stokes equations may be chosen as the initial guess for the quadratic convergence of Newton's algorithm applied to Navier-Stokes equations provided there are sufficiently small mesh size h and the moderate Reynold's number. We provide also a mixed convergence analysis in terms of iterations and finite-error estimates of the initial guess with a regularity estimate and error analysis for each Newton's step.