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-infinity-asymptotic behavior in maximum norm is given. The approach is based on the subsolution concept and discrete regularity.