On the Newton-Kantorovich theorem and nonlinear finite element methods

Ioannis K. Argyros. "On the Newton-Kantorovich theorem and nonlinear finite element methods." Applicationes Mathematicae 36.1 (2009): 75-81. <http://eudml.org/doc/279981>.

@article{IoannisK2009,
abstract = {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.},
author = {Ioannis K. Argyros},
journal = {Applicationes Mathematicae},
keywords = {Newton-Kantorovich hypothesis; boundary value problem; nonlinear operator equation; Banach space; finite element; strongly nonlinear elliptic boundary value problem},
language = {eng},
number = {1},
pages = {75-81},
title = {On the Newton-Kantorovich theorem and nonlinear finite element methods},
url = {http://eudml.org/doc/279981},
volume = {36},
year = {2009},
}

TY - JOUR
AU - Ioannis K. Argyros
TI - On the Newton-Kantorovich theorem and nonlinear finite element methods
JO - Applicationes Mathematicae
PY - 2009
VL - 36
IS - 1
SP - 75
EP - 81
AB - 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.
LA - eng
KW - Newton-Kantorovich hypothesis; boundary value problem; nonlinear operator equation; Banach space; finite element; strongly nonlinear elliptic boundary value problem
UR - http://eudml.org/doc/279981
ER -