### 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 |

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### Keywords

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

### ASJC Scopus subject areas

- Applied Mathematics
- Computational Mathematics
- Modelling and Simulation