GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
Computer Methods in Applied Mechanics and Engineering
Approximate solution of the trust region problem by minimization over two-dimensional subspaces
Mathematical Programming: Series A and B
Hybrid Krylov methods for nonlinear systems of equations
SIAM Journal on Scientific and Statistical Computing
Mixed and hybrid finite element methods
Mixed and hybrid finite element methods
What are C and h?: inequalities for the analysis and design of finite element methods
Computer Methods in Applied Mechanics and Engineering
Stabilized finite element methods. II: The incompressible Navier-Stokes equations
Computer Methods in Applied Mechanics and Engineering
Choosing the forcing terms in an inexact Newton method
SIAM Journal on Scientific Computing - Special issue on iterative methods in numerical linear algebra; selected papers from the Colorado conference
Journal of Computational Physics
NITSOL: A Newton Iterative Solver for Nonlinear Systems
SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
An Adaptive Nonlinear Least-Squares Algorithm
ACM Transactions on Mathematical Software (TOMS)
Trust-region methods
Finite Element Method for Elliptic Problems
Finite Element Method for Elliptic Problems
A Globally Convergent Newton-GMRES Subspace Method for Systems of Nonlinear Equations
SIAM Journal on Scientific Computing
On backtracking failure in newton-GMRES methods with a demonstration for the navier-stokes equations
Journal of Computational Physics
Subspace Trust-Region Methods for Large Bound-Constrained Nonlinear Equations
SIAM Journal on Numerical Analysis
A globally convergent Newton-GMRES method for large sparse systems of nonlinear equations
Applied Numerical Mathematics
Nonsymmetric Preconditioner Updates in Newton-Krylov Methods for Nonlinear Systems
SIAM Journal on Scientific Computing
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In this work we study the numerical solution of nonlinear systems arising from stabilized FEM discretizations of Navier-Stokes equations. This is a very challenging problem and often inexact Newton solvers present severe difficulties to converge. Then, they must be wrapped into a globalization strategy. We consider the classical backtracking procedure, a subspace trust-region strategy and an hybrid approach. This latter strategy is proposed with the aim of improve the robustness of backtracking and it is obtained combining the backtracking procedure and the elliptical subspace trust-region strategy. Under standard assumptions, we prove global and fast convergence of the inexact Newton methods embedded in this new strategy as well as in the subspace trust-region procedure. Computational results on classical CFD benchmarks are performed. Comparisons among the classical backtracking strategy, the elliptical subspace trust-region approach and the hybrid procedure are presented. Our numerical experiments show the effectiveness of the proposed hybrid technique.