Convergence of iterative methods in penalty finite element approximation of the Navier-Stokes equations

Abstract Sufficient conditions for convergence are established here for some common iterative methods applied to a penalty finite element formulation of the Navier-Stokes equations. The methods analyzed are iterative linearization, successive approximation, Newton's method, and certain standard modifications of Newton's method. The results are obtained under assumptions on the data that ensure that a unique solution exists. Supporting numerical experiments, including a study of the effect of the penalty parameter and finite precision arithmetic on the iteration convergence, are described.