Parameter identification in stationary groundwater flow problems in drainage basins

We discuss the recovery of some parameters in an elliptic boundary value problem, which models a specific stationary flow problem in drainage basins, by using the measured values of the hydraulic head in discrete points through the physical domain. The underlying direct problem is the one considered by Tòth (J. Geophys. Res. 67 (1962) 4375; 67 (1963) 4795), among others. The inverse problem is solved by means of the Levenberg–Marquardt method (in: G.A. Watson (Ed.), Numerical Analysis, Lecture Notes in Mathematics, Vol. 630, Springer, Berlin, New York, 1977, pp. 105–116). We also show how the infinite element method allows the identification of the far field value of the hydraulic head.