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This paper deals with the numerical analysis of the problem of parabolic quasi-variational inequalities related to impulse control problems. An optimal L -convergence of a piecewise linear finite element method is established using the concept of subsolution. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

This paper is an extension and generalization of the previous results, cf. [2-4]. It is devoted to the theta-scheme with respect to the t -variable combined with a finite-element spatial approximation of the evolutionary Hamilton-Jacobi-Bellman equations (HJB equation) and involves a weakly coupled discrete system of parabolic quasi-variational inequalities (PQVs). Its relation to time energy behavior is proved. In addition, the PQVs are transformed into a coercive discrete system of elliptic quasi-variational inequalities. A new iterative discrete algorithm is also proposed to show the existence and uniqueness of the discrete solution. Moreover, its convergence is established. Then a simple proof to an asymptotic behavior in uniform norm is given. Furthermore the proposed approach is based on a discrete L-stability property with respect to the right-hand side and the boundary conditions. [ABSTRACT FROM AUTHOR]