Skip to main content

Advertisement

SpringerLink
Log in

L ∞-Error Analysis for Parabolic Quasi-Variational Inequalities Related to Impulse Control Problems

  • Published:
Computational Mathematics and Modeling Aims and scope Submit manuscript

This paper deals with the numerical analysis of the problem of parabolic quasi-variational inequalities related to impulse control problems. An optimal L ∞-convergence of a piecewise linear finite element method is established using the concept of subsolution.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. A. Achdou, F. Hecht, and D. Pommier, “A posteriori error estimates for parabolic variational inequalities,” J. Sci. Comput. Math. Appl., 37, 336–366 (2008).

    MathSciNet  MATH  Google Scholar 

  2. Alfredo Fetter, “L ∞-error estimate for an approximation of a parabolic variational inequality,” Numer. Math., 50, 557–565 (1987).

  3. A. Bensoussan and J. L. Lions, “Contrôle impulsionnel et in équations quasi-variationnelles d’évolution,” Centre Recherche. Acad. Sci., 276, 1333–1338 (1973).

    MathSciNet  MATH  Google Scholar 

  4. A. Bensoussan and J. L. Lions, Applications des in équations variationnelles en contrôle stochastique, Dunod, Paris (1982).

  5. M. Boulbrachene, “The noncoercive quasi-variational inequalities related to impulse control problems,” Comput. Math. Appl., 35, 101–108 (1998).

    Article  MathSciNet  MATH  Google Scholar 

  6. M. Boulbrachene, “On variational inequalities with vanishing zero term,” J. Inequalities Appl., 2013:438. doi:10.1186/1029-242X-2013-438 (2013).

    MathSciNet  MATH  Google Scholar 

  7. M. A. Bencheikh Le Hocine, and M. Haiour, “Algorithmic approach for the aysmptotic behavior of a system of parabolic quasi variational inequalities,” Appl. Math. Sci., 7, 909–921 (2013).

    Article  MathSciNet  Google Scholar 

  8. Mohamed Amine Bencheikh Le Hocine, Salah Boulaaras, and Mohamed Haiour, “An optimal L ∞-error estimate for an approximation of a parabolic variational inequality,” Numer. Funct. Anal. Optim., 37, 1–18 (2016).

  9. Salah Boulaaras,Med Amine Bencheikh le Hocine, and Mohamed Haiour, “The finite element approximation in a system of parabolic quasi-variational inequalities related to management of energy production with mixed boundary condition,” Comput. Math. Model., 25, 530–543 (2014).

  10. S. Boulaaras and M. Haiour, “L ∞-asymptotic behavior for a finite element approximation in parabolic quasi-variational inequalities related to impulse control problem,” Appl. Math. Comput., 217, 6443–6450 (2011).

    MathSciNet  MATH  Google Scholar 

  11. A. Berger and R. Falk, “An error estimate for the truncation method for the solution of parabolic obstacle variational inequalities,” Math. Comput., 31, 619–628 (1977).

    Article  MathSciNet  MATH  Google Scholar 

  12. H. Brezis, “Problemes unilateraux,” J. Math. Pures Appl., 5, 1–168 (1972).

    MathSciNet  MATH  Google Scholar 

  13. P. Cortey-Dumont, “On the finite element approximation in the L ∞-norm of variational inequalities with nonlinear operators,” Numer. Math., 47, 45–57 (1985).

    Article  MathSciNet  MATH  Google Scholar 

  14. P. Cortey-Dumont, “Approximation numerique d’une inequation quasi-variationnelle liee a des problemes de gestion de stock,” RAIRO Anal. Numer., 14, 45–57 (1980).

    MathSciNet  MATH  Google Scholar 

  15. P. Cortey-Dumont, “On finite element approximation in the L ∞-norm of parabolic obstacle variational inequalities and quasivariational inequalities,” in: Rapport Interne 112, CMA. Ecole Polytechnique, Palaiseau, France.

  16. P. G. Ciarlet and P. A. Raviart, “Maximum principle and uniform convergence for the finite element method,” Comp. Methods Appl. Mech. Eng., 2, l–20 (1973).

  17. I. Diaz and J. Defonso, “On a Fully non-linear parabolic equation and the asymptotic behavior of its solution,” J. Math. Anal. Appl., 95, 144–168 (1985).

    Article  Google Scholar 

  18. C. Johnson, “A convergence estimate for an approximation of a parabolic variational inequality,” SIAM J. Numer. Anal., 13, 599–606 (1976).

    Article  MathSciNet  MATH  Google Scholar 

  19. J. Nitsche, “L ∞-convergence of finite element approximations, In Mathematical Aspects of Finite Element Methods,” Lect. Notes Math., 606, 261–274 (1977).

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Tamanghesset University Center, B.P. 10034, Sersouf, Tamanghesset, 11000, Algeria

    Mohamed El Amine Bencheikh Le Hocine

  2. LMAM Laboratory, 08 May 1945 University, Guelma, 2400, Algeria

    Mohamed El Amine Bencheikh Le Hocine

  3. LANOS Laboratory, Department Of Mathematics, Faculty Of Sciences, Badji Mokhtar University, B.P 12, Annaba, 23000, Algeria

    Mohamed Haiour

Authors
  1. Mohamed El Amine Bencheikh Le Hocine
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mohamed Haiour
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mohamed El Amine Bencheikh Le Hocine.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Le Hocine, M.E.A.B., Haiour, M. L ∞-Error Analysis for Parabolic Quasi-Variational Inequalities Related to Impulse Control Problems. Comput Math Model 28, 89–108 (2017). https://doi.org/10.1007/s10598-016-9349-7

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10598-016-9349-7

Keywords

Search

Navigation