### 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 language | English |
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Pages (from-to) | 17-27 |

Number of pages | 11 |

Journal | Computers and Mathematics with Applications |

Volume | 39 |

Issue number | 7-8 |

Publication status | Published - Mar 1 2000 |

### Fingerprint

### 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.

Research output: Contribution to journal › Article

*Computers and Mathematics with Applications*, vol. 39, no. 7-8, pp. 17-27.

}

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 -