Green element method solutions to steady inverse contaminant transport problems

Inverse contaminant transport problems, unlike direct problems, may result in non-unique and unstable solutions because of the ill-conditioned nature of the coefficient matrix. In this work the Green element method (GEM) is used to solve steady inverse contaminant transport problems. The ill-conditioned, overdetermined system of equations that arises from the Green element discretization is solved by the least square method with the singular value decomposition technique and Tikhonov regularization. Two examples of steady inverse contaminant transport problems with constant and variable velocity are simulated by GEM with good prediction obtained for the concentration and fluxes.