PRECONDITIONED NEWTON METHODS USING INCREMENTAL UNKNOWNS METHODS FOR THE RESOLUTION OF A STEADY-STATE NAVIER-STOKES-LIKE PROBLEM

In a previous work, one of the authors has studied a numerical treatme nt (by fully implicit discretizations) of a two-dimensional Navier-Sto kes-like problem and has proved existence and convergence results for the resulting discretized systems with homogeneous Dirichlet boundary conditions. In this work, we propose some new preconditioned multileve l versions of inexact-Newton algorithms to solve these equations. We a lso develop another multilevel preconditioner for a nonlinear GMRES al gorithm. All of the preconditioners are based on incremental unknowns formulations. (C) Elsevier Science Inc., 1997.