### Abstract

We establish optimal L^{∞}-error estimate for a class of variational inequalities (VIs) with nonlinear source term, using a very simple argument mainly based on the discrete L^{∞}-stability property with respect to the right-hand side in elliptic VIs. We also show that the same approach extends to the corresponding noncoercive problems and optimal uniform convergence order is obtained as well.

Original language | English |
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Pages (from-to) | 1013-1017 |

Number of pages | 5 |

Journal | Applied Mathematics Letters |

Volume | 15 |

Issue number | 8 |

Publication status | Published - Nov 2002 |

### Fingerprint

### Keywords

- Finite element
- L-error estimate
- L-stability
- Nonlinear source term
- Variational inequalities

### ASJC Scopus subject areas

- Computational Mechanics
- Control and Systems Engineering
- Applied Mathematics
- Numerical Analysis

### Cite this

**Optimal L∞-error estimate for variational inequalities with nonlinear source terms.** / Boulbrachene, M.

Research output: Contribution to journal › Article

*Applied Mathematics Letters*, vol. 15, no. 8, pp. 1013-1017.

}

TY - JOUR

T1 - Optimal L∞-error estimate for variational inequalities with nonlinear source terms

AU - Boulbrachene, M.

PY - 2002/11

Y1 - 2002/11

N2 - We establish optimal L∞-error estimate for a class of variational inequalities (VIs) with nonlinear source term, using a very simple argument mainly based on the discrete L∞-stability property with respect to the right-hand side in elliptic VIs. We also show that the same approach extends to the corresponding noncoercive problems and optimal uniform convergence order is obtained as well.

AB - We establish optimal L∞-error estimate for a class of variational inequalities (VIs) with nonlinear source term, using a very simple argument mainly based on the discrete L∞-stability property with respect to the right-hand side in elliptic VIs. We also show that the same approach extends to the corresponding noncoercive problems and optimal uniform convergence order is obtained as well.

KW - Finite element

KW - L-error estimate

KW - L-stability

KW - Nonlinear source term

KW - Variational inequalities

UR - http://www.scopus.com/inward/record.url?scp=31244434147&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=31244434147&partnerID=8YFLogxK

M3 - Article

VL - 15

SP - 1013

EP - 1017

JO - Applied Mathematics Letters

JF - Applied Mathematics Letters

SN - 0893-9659

IS - 8

ER -