An application of the Kantorovich theorem to nonlinear finite element analysis
type: Item
instance of: scholarly article
title: An application of the Kantorovich theorem to nonlinear finite element analysis
zbMATH Open document ID: 0942.65056
author: Takuya Tsuchiya
published in: Numerische Mathematik
publication date: 2000-04-10T00:00:00Z
review text: The author proves the existence as well as a priori error estimates for a finite element solution to a nonlinear problem by means of the Kantorovich theorem. This theorem is more known in the context of the numerical solution using Newton's iteration. The problem under consideration covers elliptic boundary value problems in 1, 2, or 3 dimensions with a strong nonlinearity: Find \(u= u(x)\) such that \[ \text{div }a(x,u, \text{grad }u)= f(x,u, \text{grad }u). \]
Mathematics Subject Classification ID: 65J15
Mathematics Subject Classification ID: 65N15
Mathematics Subject Classification ID: 35J65
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 47J25
zbMATH DE Number: 1398750
zbMATH Keywords: error estimates
zbMATH Keywords: finite element
zbMATH Keywords: Kantorovich theorem
zbMATH Keywords: elliptic boundary value problems
zbMATH Keywords: strong nonlinearity
reviewed by: Etienne Emmrich
MaRDI profile type: Publication
full work available at URL: s002110050466
OpenAlex ID: W1990201180
DOI: 10.1007/S002110050466
description: scientific article; zbMATH DE number 1398750