We study the numerical aspect of the optimal control of problems governed by a linear elliptic partial differential equation (PDE). We consider here the gas flow in porous media. The observed variable is the flow field we want to maximize in a given part of the domain or its boundary. The control variable is the pressure at one part of the boundary or the discharges of some wells located in the interior of the domain. The objective functional is a balance between the norm of the flux in the observation region and the costs due to the control variables. We consider several geometric configurations of the control and the observation variables, and we make use of different objective functionals. We take advantage of the linearity of the flux w.r.t. the control variable to significantly reduce the computational effort and to deduce the optimal controls of wide class of objective functionals. In this paper we consider the deterministic case where the model parameters are given in the whole domain.
@article{urn:eudml:doc:44456,
title = {Optimal control of fluid flow in soil 1. Deterministic case.},
journal = {Revista Matem\'atica de la Universidad Complutense de Madrid},
volume = {11},
year = {1998},
pages = {373-401},
zbl = {0937.49014},
mrnumber = {MR1666501},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:44456}
}
Kelanemer, Youcef. Optimal control of fluid flow in soil 1. Deterministic case.. Revista Matemática de la Universidad Complutense de Madrid, Tome 11 (1998) pp. 373-401. http://gdmltest.u-ga.fr/item/urn:eudml:doc:44456/