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.