An inexact Newton method with inner preconditioned CG for non-uniformly monotone elliptic problems - Borsos, Benjámin (Mathematical Modelling and Analysis, 2021)
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.