Geodesic
$L^\infty -$Asymptotic Behavior of a Finite Element Method for a System of Parabolic Quasi-Variational Inequalities with Nonlinear Source Terms
Kragujevac Journal of Mathematics, Tome 47 (2023) no. 3, p. 347 .

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This paper is an extension and a generalization of the previous results, cf. \cite{DC,Benc,sal,Bench}. It is devoted to studying the finite element approximation of the non coercive system of parabolic quasi-variational inequalities related to the management of energy production problem. Specifically, we prove optimal $L^{\infty }$-asymptotic behavior of the system of evolutionary quasi-variational inequalities with nonlinear source terms using the finite element spatial approximation and the subsolutions method.
Classification : 65J15 65N30
Keywords: Quasi-variational inequalities, asymptotic behavior, subsolutions method, finite elements approximation, $L^\infty $-error estimate 
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     author = {Djaber Chemseddine Benchettah},
     title = {$L^\infty -${Asymptotic} {Behavior} of a {Finite} {Element} {Method} for a {System} of {Parabolic} {Quasi-Variational} {Inequalities} with {Nonlinear} {Source} {Terms}},
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Djaber Chemseddine Benchettah. $L^\infty -$Asymptotic Behavior of a Finite Element Method for a System of Parabolic Quasi-Variational Inequalities with Nonlinear Source Terms. Kragujevac Journal of Mathematics, Tome 47 (2023) no. 3, p. 347 . http://geodesic.mathdoc.fr/item/KJM_2023_47_3_a1/