Steady filtration problems with seawater intrusion: Penalized finite element approximations Original Research Article

Penalized finite element approximations of steady filtration problems are studied for a general section of an open aquifer with seawater intrusion. The corresponding variational model is the one proposed and analyzed in (G. Alduncin, J. Esquivel-Avila, L. Reyes-Avila, Comput. Methods Appl. Mech. Engrg. 151 (1998) 13–25), which characterizes a two-free boundary problem in terms of a nonsubdifferential inequality. Convergence of conforming finite element approximations is established, and for numerical stabilization, the Tabata upwind technique is applied. For resolution purposes, the resulting discrete nonlinear penalized model is characterized by a fixed-point problem, and an iterative algorithm is considered. Finally, some numerical applications exemplify the theory.