On Mesh-Independent Convergence of an Inexact Newton-Multigrid Algorithm

In this paper we revisit and prove optimal order and mesh–independent convergence of an inexact Newton method where the linear Jacobian systems are solved with multigrid techniques. This convergence is shown using Banach spaces and the norm, max{‖ · ‖1, ‖ · ‖0,∞}, a stronger norm than is used in previous work. These results are valid for a class of second order, semi–linear, finite element, elliptic problems posed on quasi–uniform grids. Numerical results are given which validate the theory.