The aim of this paper is to compare and realize three efficient iterative methods, which have mesh independent convergence, and to propose some improvements for them. We look for the numerical solution of a nonlinear model problem using FEM discretization with gradient and Newton type methods. Three numerical methods have been carried out, namely, the gradient, Newton and quasi-Newton methods. We have solved the model problem with these methods, we have investigated the differences between them and analyzed their behavior, efficiency and mesh independence. We also compare the theoretical results to the numerical ones, and finally we propose some improvements which we also investigate.
@article{bwmeta1.element.doi-10_2478_s11533-011-0071-6,
author = {Bal\'azs Kov\'acs},
title = {A comparison of some efficient numerical methods for a nonlinear elliptic problem},
journal = {Open Mathematics},
volume = {10},
year = {2012},
pages = {217-230},
zbl = {1247.65148},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-011-0071-6}
}
Balázs Kovács. A comparison of some efficient numerical methods for a nonlinear elliptic problem. Open Mathematics, Tome 10 (2012) pp. 217-230. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-011-0071-6/
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