A Game Theory Approach for the Groundwater Pollution Control

A scheme is proposed for the numerical study of optimal control problems related to groundwater quality management in the case of nonpoint-source pollution. The corresponding state equation is a system of coupled nonlinear partial differential equations. The approximation is given by a finite volume scheme based on a two-point flux approximation with upwind mobilities embedded in an iterative fixed point approximation. The analysis of the convergence of the scheme allows to establish existence and uniqueness results under reasonable assumptions. Numerical illustrations of the performance of the algorithm are given in realistic situations.