On a numerical approximation of a highly nonlinear parabolic inverse problem in hydrology
In this paper, we consider an inverse problem in hydrology governed by a highly nonlinear parabolic equation called Richards equation. This inverse problem consists to determine a set of hydrological parameters describing the flow of water in porous media, from some additional observations on pressure. We propose an approximation method of this problem based on its optimal control formulation and a temporal discretization of its state problem. The obtained discrete nonlinear state problem is approached by the finite difference method and solved by Picard's method. Then, for the resolution of the discrete associated optimization problem, we opt for an evolutionary algorithm. Finally, we give some numerical results showing the efficiency of the proposed approach.