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