Table of Contents
ISRN Mathematical Analysis
Volume 2011, Article ID 703670, 15 pages
http://dx.doi.org/10.5402/2011/703670
Research Article

A New Approach to Asymptotic Behavior for a Finite Element Approximation in Parabolic Variational Inequalities

1Hydrometeorological Institute of Formation and Research, Box. 7019, Seddikia, Oran 31000, Algeria
2Department of Mathematics, Faculty of Science, University of Annaba, Box. 12, Annaba 23000, Algeria

Received 30 March 2011; Accepted 13 May 2011

Academic Editors: G. Garcea and S. Zhang

Copyright © 2011 Salah Boulaaras and Mohamed Haiour. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. A. Bensoussan and J.-L. Lions, Applications des Inéquations Variationnelles en Contrôle Stochastique, Dunod, Paris, Frnace, 1978. View at Zentralblatt MATH
  2. M. Boulbrachene, “Pointwise error estimates for a class of elliptic quasi-variational inequalities with nonlinear source terms,” Applied Mathematics and Computation, vol. 161, no. 1, pp. 129–138, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  3. M. Boulbrachene, “Optimal L-error estimate for variational inequalities with nonlinear source terms,” Applied Mathematics Letters, vol. 15, no. 8, pp. 1013–1017, 2002. View at Publisher · View at Google Scholar
  4. S. Boulaaras and M. Haiour, “L-asymptotic bhavior for a finite element approximation in para- bolic quasi-variational inequalities related to impulse control problem,” Applied Mathematics and Computation, vol. 217, no. 14, pp. 6443–6450, 2011. View at Publisher · View at Google Scholar
  5. P. Cortey-Dumont, “On finite element approximation in the L-norm parabolic obstacle vari-ational and quasivariational inequalities,” Rapport Interne 112, CMA. Ecole Polytechnique, Palaiseau, France.
  6. P. Cortey-Dumont, “On finite element approximation in the L-norm of variational inequalities,” Numerische Mathematik, vol. 47, no. 1, pp. 45–57, 1985. View at Publisher · View at Google Scholar
  7. P. Cortey-Dumont, “Approximation numérique d'une inéquation quasi variationnelle liée à des problèmes de gestion de stock,” RAIRO—Analyse Numérique, vol. 14, no. 4, pp. 335–346, 1980. View at Google Scholar · View at Zentralblatt MATH
  8. M. Haiour and S. Boulaaras, “Uniform convergence of schwarz method for elliptic quasi-variational inequalities related to impulse control problem,” An-Najah University Journal for Research, vol. 24, pp. 71–89, 2010. View at Google Scholar
  9. J.-L. Lions and G. Stampacchia, “Variational inequalities,” Communications on Pure and Applied Mathematics, vol. 20, pp. 493–519, 1967. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  10. P. G. Ciarlet and P.-A. Raviart, “Maximum principle and uniform convergence for the finite element method,” Computer Methods in Applied Mechanics and Engineering, vol. 2, no. 1, pp. 17–31, 1973. View at Publisher · View at Google Scholar · View at Zentralblatt MATH