On the global existence for a degenerate elliptic–parabolic seawater intrusion problem

We studied a sharp interface model issuing from a seawater intrusion problem in a confined aquifer. This model consists in a coupled system of an elliptic and a de-generate parabolic equation. The global in time existence is obtained in using Schauder theorem combined with parabolic regularization. We establish a priori estimations for the P1 finite element method applied to this problem. Finally, we propose numerical simulations in easy examples.