Adaptive and formfree identification of nonlinearities in fluid flow from column experiments - Bitterlich, Sandro; Knabner, Peter (Fluid flow and transport in porous media: mathematical and numerical treatment, 2002)
"Fluid flow through an unsaturated soil is described by a model equation which contains the hydraulic properties of the considered medium in the form of nonlinear coefficient functions. A common method to determine the hydraulic properties is based on the formulation and solution of an inverse problem for soil column outflow experiments. Here, a formfree approach and a numerical least squares technique in combination with a stability analysis of the inverse problem is used for the determination of the nonlinearities. In accordance with Tikhonov regularization techniques, penalty terms, which can be added to the least squares functional, are derived.''