On the numerical analysis of some variational problems with nonhomogeneous boundary conditions
type: Item
instance of: scholarly article
title: On the numerical analysis of some variational problems with nonhomogeneous boundary conditions
zbMATH Open document ID: 0922.65049
DOI: 10.1007/BF03167317
author: Michel Chipot
author: A. Elfanni
published in: Japan Journal of Industrial and Applied Mathematics
publication date: 1999-10-11T00:00:00Z
review text: This paper introduces a new technique to get energy estimates for non-convex problems, with nonlinear boundary conditions in terms of the mesh size in a finite elements scheme. A possible physical setting for the problem is a function \(\phi:\mathbb{R}^n\to \mathbb{R}\) which may be interpreted as a stored energy density that vanishes at various points in \(\mathbb{R}^n\). The essential theorems are given in Section 2 of the paper, where error bounds of the form \(Ch^p\) are obtained where \(p=1/2\), \(q/(1+ 1)\) or \(r/(r+1)\) and where \(C\) is independent of \(h\). Here, \(q>0\) is specified in the problem and \(r\) is the infimum of \(q\) and \(1\).
Mathematics Subject Classification ID: 65K10
Mathematics Subject Classification ID: 49J20
Mathematics Subject Classification ID: 49M15
zbMATH DE Number: 1239885
zbMATH Keywords: variational problems
zbMATH Keywords: nonhomogeneous boundary conditions
zbMATH Keywords: finite elements
zbMATH Keywords: error bounds
reviewed by: Brian L. Burrows
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf03167317
OpenAlex ID: W1968405546
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description: scientific article; zbMATH DE number 1239885