Finite element approximation of a nonlinear elliptic equation arising from bimaterial problems in elastic-plastic mechanics
type: Item
instance of: scholarly article
title: Finite element approximation of a nonlinear elliptic equation arising from bimaterial problems in elastic-plastic mechanics
zbMATH Open document ID: 0971.65103
published in: Numerische Mathematik
publication date: 2001-10-26T00:00:00Z
review text: The author considers a quasilinear Dirichlet problem for \(\operatorname{div} (k \operatorname{grad} u) + f = 0\) in a two-dimensional Lipschitz domain \(\Omega\) which consists of two subdomains. Here \(k\) depends on \(|\operatorname {grad} u |\) and may be different for the two subdomains. To study the accuracy of a conforming linear finite element method on a regular triangulation, and defining \[ a(u,w):=\int_\Omega k(|\operatorname{grad} u|)\operatorname{grad} u\cdot\operatorname{grad} w, \] as the distance of \(u\) and \(v\) the expression \(a(u,u-v)-a(v,u-v)\) is taken and shown to be equivalent to a certain quasi-norm. This leads to optimal error bounds for sufficiently regular solutions.
reviewed by: Gisbert Stoyan
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 35J65
Mathematics Subject Classification ID: 74C05
Mathematics Subject Classification ID: 65N15
Mathematics Subject Classification ID: 74S05
zbMATH DE Number: 1538609
zbMATH Keywords: bimaterial problems
zbMATH Keywords: quasi-norm
zbMATH Keywords: elastic-plastic mechanics
zbMATH Keywords: quasilinear elliptic equation
zbMATH Keywords: quasilinear Dirichlet problem
zbMATH Keywords: conforming linear finite element method
zbMATH Keywords: error bounds
author: Wenbin Liu
MaRDI profile type: Publication
full work available at URL: s002110000157
OpenAlex ID: W2123797539
DOI: 10.1007/S002110000157
description: scientific article; zbMATH DE number 1538609