A fixed-point approximation method for some noncoercive variational problems

Research output: Contribution to journalArticle

Abstract

This paper deals with the finite-element approximation of some variational problems, namely, linear elliptic boundary value problems, variational inequalities, and quasi-variational inequalities with noncoercive operators. To prove optimal L -error estimates, we introduce a simple and direct argument combining continuous piecewise linear finite elements with the Banach fixed-point theorem.

Original languageEnglish
Pages (from-to)17-27
Number of pages11
JournalComputers and Mathematics with Applications
Volume39
Issue number7-8
Publication statusPublished - Mar 1 2000

Fingerprint

Banach Fixed Point Theorem
Fixed Point Method
Quasi-variational Inequalities
Elliptic Boundary Value Problems
Finite Element Approximation
Variational Problem
Approximation Methods
Piecewise Linear
Variational Inequalities
Boundary value problems
Error Estimates
Finite Element
Operator

Keywords

  • Boundary value problem
  • Finite element
  • Fixed point
  • Quasi-variational inequality
  • Variational inequality

ASJC Scopus subject areas

  • Applied Mathematics
  • Computational Mathematics
  • Modelling and Simulation

Cite this

A fixed-point approximation method for some noncoercive variational problems. / Boulbrachene, M.

In: Computers and Mathematics with Applications, Vol. 39, No. 7-8, 01.03.2000, p. 17-27.

Research output: Contribution to journalArticle

@article{cb5daefeb3bf495dbdd754b9c120f42b,
title = "A fixed-point approximation method for some noncoercive variational problems",
abstract = "This paper deals with the finite-element approximation of some variational problems, namely, linear elliptic boundary value problems, variational inequalities, and quasi-variational inequalities with noncoercive operators. To prove optimal L ∞-error estimates, we introduce a simple and direct argument combining continuous piecewise linear finite elements with the Banach fixed-point theorem.",
keywords = "Boundary value problem, Finite element, Fixed point, Quasi-variational inequality, Variational inequality",
author = "M. Boulbrachene",
year = "2000",
month = "3",
day = "1",
language = "English",
volume = "39",
pages = "17--27",
journal = "Computers and Mathematics with Applications",
issn = "0898-1221",
publisher = "Elsevier Limited",
number = "7-8",

}

TY - JOUR

T1 - A fixed-point approximation method for some noncoercive variational problems

AU - Boulbrachene, M.

PY - 2000/3/1

Y1 - 2000/3/1

N2 - This paper deals with the finite-element approximation of some variational problems, namely, linear elliptic boundary value problems, variational inequalities, and quasi-variational inequalities with noncoercive operators. To prove optimal L ∞-error estimates, we introduce a simple and direct argument combining continuous piecewise linear finite elements with the Banach fixed-point theorem.

AB - This paper deals with the finite-element approximation of some variational problems, namely, linear elliptic boundary value problems, variational inequalities, and quasi-variational inequalities with noncoercive operators. To prove optimal L ∞-error estimates, we introduce a simple and direct argument combining continuous piecewise linear finite elements with the Banach fixed-point theorem.

KW - Boundary value problem

KW - Finite element

KW - Fixed point

KW - Quasi-variational inequality

KW - Variational inequality

UR - http://www.scopus.com/inward/record.url?scp=0034174004&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0034174004&partnerID=8YFLogxK

M3 - Article

VL - 39

SP - 17

EP - 27

JO - Computers and Mathematics with Applications

JF - Computers and Mathematics with Applications

SN - 0898-1221

IS - 7-8

ER -