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A new proof for the existence and uniqueness of the discrete evolutionary HJB equations
Journal article   Peer reviewed

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

Salah Boulaaras and Mohamed Haiour
Applied mathematics and computation, Vol.262, pp.42-55
01/07/2015
DOI: https://doi.org/10.1016/j.amc.2015.03.095

Abstract

Finite elements HJB equations QVIs Theta scheme fixed point
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.

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