Inexact Newton-type methods for non-linear problems arising from the SUPG/PSPG solution of steady incompressible navier-stokes equations

Abstract

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, associated with the SUPG/PSPG stabilized finite element formulation. The resulting systems of equations are solved iteratively by a preconditioned Krylov-space method such as GMRES. Numerical experiments are shown to validate our approach. Performance of the nonlinear strategies is accessed by numerical tests. We concluded that Inexact Newton-type methods are more efficient than conventional Newton-type methods

Augmented Stabilized and Galerkin Least Squares Formulations

“…Let us denote the Jacobian matrix by J ∈ ℜ N . Classical Newton's method for solving the non-linear problem can be enunciated as (Elias et al, 2004(Elias et al, , 2006 for k = 0 until convergence…”

Globalization strategies for Newton–Krylov methods for stabilized FEM discretization of Navier–Stokes equations

“…Recently, there has been much research in investigating the convergence behaviour of globalized Newton-Krylov methods applied to the nonlinear systems arising in the solution of fully coupled large scale CFD problems [14,25,29,30]. In fact, in these papers it has been shown that the numerical solution of these nonlinear systems is very challenging and a globalization strategy is needed in order to successfully solve this class of problems.…”