Using a weaker version of the Newton-Kantorovich theorem, we provide a discretization result to find finite element solutions of elliptic boundary value problems. Our hypotheses are weaker and under the same computational cost lead to finer estimates on the distances involved and a more precise information on the location of the solution than before.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-am36-1-6,
author = {Ioannis K. Argyros},
title = {On the Newton-Kantorovich theorem and nonlinear finite element methods},
journal = {Applicationes Mathematicae},
volume = {36},
year = {2009},
pages = {75-81},
zbl = {1169.65044},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am36-1-6}
}
Ioannis K. Argyros. On the Newton-Kantorovich theorem and nonlinear finite element methods. Applicationes Mathematicae, Tome 36 (2009) pp. 75-81. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am36-1-6/