Inexact Newton-Type Methods for Non-Linear Problems Arising from the SUPG/PSPG Solution of Steady Incompressible Navier-Stokes Equations

The finite element discretization of the incompressible steady-state Navier- Stokes equations yields a non-linear problem, due to the convective terms in the momentum equations. Several methods may be used to solve this non-linear problem. In this work we study Inexact Newton-type methods with backtracking, associated to the SUPG/PSPG stabilized finite element formulation. The resulting systems of equations are solved iteratively by Krylov-Space methods such as GMRES, TFQMR and BiCGSTAB, with three different preconditioners. Numerical experiments are show to validate our approach. Performance of the iterative solvers and of the nonlinear strategies are accessed also by numerical tests. We concluded that the Inexact Newton-type are more efficient than conventional Newton-Type methods.