Open AccessAN INEXACT NEWTON METHOD WITH INNER PRECONDITIONED CG FOR NON-UNIFORMLY MONOTONE ELLIPTIC PROBLEMS
Author(s) -
Benjámin Borsos
Publication year - 2021
Publication title -
mathematical modelling and analysis/mathematical modeling and analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.491
H-Index - 25
eISSN - 1648-3510
pISSN - 1392-6292
DOI - 10.3846/mma.2021.12899
Subject(s) - mathematics , monotone polygon , conjugate gradient method , banach space , convergence (economics) , cover (algebra) , newton's method , mathematical analysis , mathematical optimization , nonlinear system , geometry , mechanical engineering , physics , quantum mechanics , engineering , economics , economic growth
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.