\(L^{\infty }\)-error estimate of a parabolic quasi-variational inequalities systems related to management of energy production problems via the subsolution concept

  • Salah Boulaaras
  • Mohamed El Amine Bencheikh Le Hocine
  • Mohamed Haiour
Original Article
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Abstract

The main propose of this paper is to provide an error estimate on uniform norm of the parabolic quasi-variational inequalities system related to management of energy production problems, using semi-implicit time scheme with Galerkin spatial methods. Moreover, a new proof of the existence and uniqueness of the solution are given by the introduction of a constructive presented algorithm. Furthermore, an optimally \(L^{\infty }\)-asymptotic behavior in maximum norm is given. The approach is based on the subsolution concept and discrete regularity.

Keywords

Parabolic quasi-variational inequalities Finite element methods Subsolutions method \(L^{\infty }\)-Asymptotic Behavior 

Mathematics Subject Classification

35 R 35 49 J 40 
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Notes

Acknowledgements

The authors would like to thank the handling editor and anonymous referee for his/her careful reading and for relevant remarks/suggestions which helped them to improve the paper. The first author gratefully acknowledge Qassim University in Kingdom of Saudi Arabia.

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Copyright information

© Sociedad Matemática Mexicana 2017

Authors and Affiliations

  • Salah Boulaaras
    • 1
    • 2
  • Mohamed El Amine Bencheikh Le Hocine
    • 3
    • 4
  • Mohamed Haiour
    • 5
  1. 1.Department of Mathematics, College of Sciences and ArtsQassim UniversityAl-RasKingdom of Saudi Arabia
  2. 2.Laboratory of Fundamental and Applied Mathematics of Oran (LMFAO) University of Oran 1Ahmed BenbellaAlgeria
  3. 3.Tamanghesset University CenterSersouf, TamanghessetAlgeria
  4. 4.LMAM Laboratory, 08 May 1945 UniversityGuelmaAlgeria
  5. 5.LANOS Laboratory, Department of Mathematics, Faculty of SciencesBadji Mokhtar UniversityAnnabaAlgeria

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