Computational Mathematics and Modeling

, Volume 25, Issue 4, pp 530–543 | Cite as

The Finite Element Approximation in a System of Parabolic Quasi-Variational Inequalities Related to Management of Energy Production with Mixed Boundary Condition

  • Salah Boulaaras
  • Med Amine Bencheikh le Hocine
  • Mohamed Haiour
Article

This paper deals with a system of parabolic quasi-variational inequalities related to the management of energy production with mixed boundary condition. A quasi-optimal L-error estimate is established using a new discrete algorithm based on a theta time scheme combined with a finite element spatial approximation. Our approach stands on a discrete L-stability property with respect to the right-hand side.

Keywords

PQVI impulse control problem L-stability analysis asymptotic behavior 

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References

  1. 1.
    A. Bensoussan and J. L. Lions, Application des Inéquations Variationnelles en Contrôle Stochastique, Dunod, Paris (1978).Google Scholar
  2. 2.
    S. Boulaaras and M. Haiour, “The finite element approximation of evolutionary Hamilton–Jacobi–Bellman equation with linear source terms,” Computational and Mathematical Modeling, Accepted 2013.Google Scholar
  3. 3.
    S. Boulaaras and M. Haiour, “Overlapping domain decomposition methods for elliptic quasi-variational inequalities related to impulse control problem with mixed boundary conditions,” Proc. Indian Acad. Sci. (Math. Sci.), 121, 481–493 (2011).MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    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).MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    S. Boulaaras and M. Haiour, “The finite element approximation of evolutionary Hamilton–Jacobi-Bellman equation with nonlinear source terms,” Indag. Math. (2012), 24, Issue 1, 161–173 (2013).MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    M. Boulbrachene, “L -Error estimate for noncoercive elliptic quasi-variational inequalities: a simple proof,” Appl. Math. E-Notes, 5, 97–102 (2005).MathSciNetMATHGoogle Scholar
  7. 7.
    P. Ciarlet and P. Raviart, “Maximum principle and uniform convergence for the finite element method,” Commun. Math. Appl. Mech. Eng., 2, 1–20 (1973).MathSciNetCrossRefGoogle Scholar
  8. 8.
    B. Perthame, “Some remarks on quasi-variational inequalities and the associated impulsive control problem,” Ann. Inst. Henri Poincare. Sect. C, 2, No. 3, 237–260 (1985).MathSciNetGoogle Scholar
  9. 9.
    R. Glowinski, J. L. Lions, and R. Tremolieres, Numerical Analysis of Variational Inequalities, North-Holland, Amsterdam (1981).MATHGoogle Scholar
  10. 10.
    P. L. Lions and B. Mercier, “Approximation numérique des equations de Hamilton Jacobi Bellman,” RAIRO, Anal. Num., 14, 369–393 (1980).MathSciNetMATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Salah Boulaaras
    • 1
  • Med Amine Bencheikh le Hocine
    • 2
  • Mohamed Haiour
    • 3
  1. 1.Department of Mathematics, College of Sciences and Arts, Al-RassEl-Qassim UniversityBuraydahKingdom of Saudi Arabia
  2. 2.Department of Mathematics and Computer ScienceTamanrasset University CenterTamanrassetAlgeria
  3. 3.Department of Mathematics, Faculty of ScienceAnnaba UniversityAnnabaAlgeria

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