Numerical Analysis of a Finite Volume Scheme for the Optimal Control of Groundwater Pollution

Choquet, Catherine; Diédhiou, Moussa Mory; Dine, Houssein Nasser El

doi:10.1007/978-3-030-43651-3_43

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2022

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“…Although we had to limit ourselves to a few examples of situations, they help to get insight into the applicability of the previous theoretical results. We adapt the tools developed in [8] for the numerical simulation of optimal control problems linked with groundwater pollution. More precisely, we compute the solution of (5.5)--(5.9) using a finite volume scheme based on a two-point flux approximation with upwind mobilities embedded in an iterative fixed point approximation.…”

Section: Main Resultmentioning

confidence: 99%

A Game Theory Approach for the Groundwater Pollution Control

Augeraud-Véron¹,

Choquet²,

Comte³

et al. 2022

SIAM J. Control Optim.

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A differential game modeling the noncooperative outcome of pollution in groundwater is studied. Spatio-temporal objectives are constrained by a convection-diffusion-reaction equation ruling the spread of the pollution in the aquifer, and the velocity of the flow solves an elliptic partial differential equation. The existence of a Nash equilibrium is proved using a fixed point strategy. A uniqueness result for the Nash equilibrium is also proved under some additional assumptions. Some numerical illustrations are provided.

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Section: Main Resultmentioning

confidence: 99%