An extension of the mesh independence principle for operator equations in Banach space Original Research Article

In this study, we extend the validity of the mesh-independence principle to include perturbed Newton-like methods in Banach space. We show that when a perturbed Newton-like method is applied to a nonlinear equation as well as to some finite-dimensional discretization of that equation, there is a difference of at most one between the number of steps required by the two processes to converge to within a given tolerance. Our results cover and extend earlier results.