$$L^{\infty }$$ L∞ -error estimate of a parabolic quasi-variational inequalities systems related to management of energy production problems via the subsolution concept

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 $$L^{\infty }$$ L∞ -asymptotic behavior in maximum norm is given. The approach is based on the subsolution concept and discrete regularity.