A new proof for the existence and uniqueness of the discrete evolutionary HJB equations

In this paper, we establish a new proof for the existence and uniqueness of the discrete solution of evolutionary HJB equations which can be approximated by a weakly coupled system of coercive elliptic quasi-variational inequalities (OVIs). For that some properties of the presented algorithm (cf., e.g., Boulaaras and Haiour, 2013; Boulbrachene and Haiour, 2001) using the theta-scheme with respect to the t-variable combined with a finite element spatial approximation are proved.