An inexact Newton method with Inner preconditioned CG for non-uniformly Monotone Elliptic Problems

The present paper introduces an inexact Newton method, coupled with a preconditioned conjugate gradient method in inner iterations, for elliptic operators with non-uniformly monotone upper and lower bounds. Convergence is proved in Banach space level. The results cover real-life classes of elliptic problems. Numerical experiments reinforce the convergence results.