Quasi-conforming finite element approximation for a fourth order variational inequality with displacement obstacle.
type: Item
instance of: scholarly article
title: Quasi-conforming finite element approximation for a fourth order variational inequality with displacement obstacle.
zbMATH Open document ID: 1034.65050
DOI: 10.1016/S0252-9602(17)30146-7
published in: Acta Mathematica Scientia. Series B. (English Edition)
publication date: 2003-09-24T00:00:00Z
review text: Let \(\Omega\) be a bounded domain of \(\mathbb{R}^{2}\) with smooth boundary \(\partial\Omega,\) \(f\in L^{2}(\Omega)\) and \(\phi\in H^{4}(\Omega)\) with \(\phi<0\) on \(\partial\Omega\). Set \(K=\{v\in H_{0}^{2}(\Omega) \mid v\geq\phi\}\) and let \(u\in K\) be a solution of the variational inequality problem \[ \int_{\Omega}\Delta u\Delta(v-u)dx\geq\int_{\Omega}f(v-u)dx,\text{\quad }\forall v\in K \] The authors apply ``unconventional quasi-conforming'' finite element approximation on the above problem. They assert to obtain error estimates which are the same as that of the conventional finite elements.
Mathematics Subject Classification ID: 65K10
Mathematics Subject Classification ID: 49J40
Mathematics Subject Classification ID: 49M15
zbMATH DE Number: 1907801
zbMATH Keywords: variational inequality
zbMATH Keywords: finite element approximation
zbMATH Keywords: displacement obstacle
zbMATH Keywords: error estimates
author: Dongyang Shi
author: Shaochun Chen
reviewed by: A. Daniilidis
MaRDI profile type: Publication
full work available at URL: s0252-9602(17)30146-7
OpenAlex ID: W2783274343
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description: scientific article; zbMATH DE number 1907801