A finite element method for a seawater intrusion problem in unconfined aquifers

We simulate a sharp-diffuse interface model issuing from a seawater intrusion problem in unconfined aquifer. We study a semi-implicite in time scheme for a Pk,(k≥1) Lagrange finite element approximation. Using the specific regularity of the exact solution, we state that the scheme is of order 1 in time and k in space. We propose a finite volume method for a regular mesh and we compare the results given by these two approximations.