Speaker
Roland Becker, Université de Pau
Abstract
Motivated by the development of adaptive finite element methods for nonlinear elliptic equations, we consider Newton’s method with updates generated on finite-dimensional subspaces. Let X and Y be reflexive Banach spaces and F differentiable from X to Y’, its derivative satisfying a local Lipschitz condition. In
order to solve F(x) = 0 we consider a globalized inexact Newton method, where the updates pk, living in Xk, are Galerkin approximations of the tangent equation in Y’k and the residual is understood as a perturbation. We propose to adapt the classical theory of inexact Newton methods to our setting in the framework of ordinary differential equations.