A finite element method for hydraulic conductivity identification in a seawater intrusion problem

This work presents a numerical method to automatically identify hydraulic conductivity in the seawater intrusion problem when a sharp interface approach is used. The mathematical formulation is based on the optimal control theory. A Lagrangian operator, whose partial derivatives provide, respectively, the state equations, the adjoint equations and the optimality condition, is introduced. The ill-posedness of the problem and the multiple minima difficulties are addressed through a combination of Tikhonov or total variation regularization with a multiscaling procedure. By numerical examples we show the effectiveness of total variation regularization for discontinuous parameters and the ability of the multiscaling approach to get the global solution.