Subsolutions, Discrete Regularity and \(L^\infty\)- Error Estimates for a Class of Elliptic QVIs: A Unified Analysis

Article Sidebar

PDF
DOI: https://doi.org/10.28924/2291-8639-24-2026-177
Published: Jun 15, 2026
Cite as:
Messaoud Boulbrachene, Subsolutions, Discrete Regularity and \(L^\infty\)- Error Estimates for a Class of Elliptic QVIs: A Unified Analysis, Int. J. Anal. Appl., 24 (2026), 177.

Main Article Content

Messaoud Boulbrachene

Abstract

We provide a unified analysis for the standard finite element approximation of a class of elliptic quasi-variational inequalities (QVIs). We also derive \(L^{\infty}\)- Error estimates combining the concepts of subsolutions and discrete regularity.

Article Details

References

  1. P. Cortey-Dumont, Approximation Numérique D'une Inéquation Quasi Variationnelle Liée à des Problèmes de Gestion de Stock, RAIRO. Anal. Numér. 14 (1980), 335–346. https://doi.org/10.1051/m2an/1980140403351.
  2. P. Cortey‐Dumont, J.C. Nedelec, Sur L'Analyse Numérique des Equations de Hamilton‐Jacobi‐Bellman, Math. Methods Appl. Sci. 9 (1987), 198–209. https://doi.org/10.1002/mma.1670090115.
  3. M. Boulbrachene, The Noncoercive Quasi-Variational Inequalities Related to Impulse Control Problems, Comput. Math. Appl. 35 (1998), 101–108. https://doi.org/10.1016/S0898-1221(98)00100-X.
  4. M. Boulbrachene, M. Haiour, The Finite Element Approximation of Hamilton-Jacobi-Bellman Equations, Comput. Math. Appl. 41 (2001), 993–1007. https://doi.org/10.1016/S0898-1221(00)00334-5.
  5. M. Boulbrachene, M. Haiour, S. Saadi, $L^infty$-Error Estimates for a System of Elliptic Quasi-Variational Inequalities, Int. J. Math. Math. Sci. 24 (2003), 1547–1561.
  6. M. Boulbrachene, Pointwise Error Estimates for a Class of Elliptic Quasi-Variational Inequalities with Nonlinear Source Terms, Appl. Math. Comput. 161 (2005), 129–138. https://doi.org/10.1016/j.amc.2003.12.015.
  7. M. Boulbrachene, P.C. Dumont, Optimal $L^infty$-Error Estimate of a Finite Element Method for Hamilton–Jacobi–Bellman Equations, Numer. Funct. Anal. Optim. 30 (2009), 421–435. https://doi.org//10.1080/01630560902987683.
  8. A. Bensoussan, J. Lions, Applications of Variational Inequalities in Stochastic Control, North Holland, (2000).
  9. A. Bensoussan, J. Lions, Impulse Control and Quasi-variational Inequalities, Gauthier-Villars, Paris, (1984).
  10. C. Lu, W. Huang, J. Qiu, Maximum Principle in Linear Finite Element Approximations of Anisotropic Diffusion-Convection-Reaction Problems, Numer. Math. 127 (2014), 515–537. https://doi.org/10.1007/s00211-013-0595-8.
  11. T. Vejchodský, The Discrete Maximum Principle for Galerkin Solutions of Elliptic Problems, Open Math. 10 (2011), 25–43. https://doi.org/10.2478/s11533-011-0085-0.
  12. P. Cortey-Dumont, On Finite Element Approximation in the $L^infty$-Norm of Variational Inequalities, Numer. Math. 47 (1985), 45–57. https://doi.org/10.1007/BF01389875.