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\(L^{\infty }\)-asymptotic behavior for a finite element approximation in parabolic quasi-variational inequalities related to impulse control problem. (English) Zbl 1211.65083
Summary: The parabolic quasi-variational inequalities are transformed into a noncoercive elliptic quasi-variational inequalities. A new iterative discrete algorithm is proposed to show the existence and uniqueness, and a simple proof to asymptotic behavior in uniform norm is also given using the theta time scheme combined with a finite element spatial approximation. The proposed approach stands on a discrete \(L^{\infty }\)-stability property with respect to the right-hand side and obstacle defined as an impulse control problem.

MSC:
65K15 Numerical methods for variational inequalities and related problems
49J40 Variational inequalities
35K86 Unilateral problems for nonlinear parabolic equations and variational inequalities with nonlinear parabolic operators
35J86 Unilateral problems for linear elliptic equations and variational inequalities with linear elliptic operators
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
49M25 Discrete approximations in optimal control
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