On backtracking failure in Newton-GMRES methods with a demonstration for the Navier-Stokes equations. (English) Zbl 1143.76489

Summary: In an earlier study of inexact Newton methods, we pointed out that certain counterintuitive behavior may occur when applying residual backtracking to the Navier-Stokes equations with heat and mass transport. Specifically, it was observed that a Newton-GMRES method globalized by backtracking (linesearch, damping) may be less robust when high accuracy is required of each linear solve in the Newton sequence than when less accuracy is required. In this brief discussion, we offer a possible explanation for this phenomenon, together with an illustrative numerical experiment involving the Navier-Stokes equations.


76M10 Finite element methods applied to problems in fluid mechanics
76M12 Finite volume methods applied to problems in fluid mechanics
76D05 Navier-Stokes equations for incompressible viscous fluids
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