Evolution Filtration Problems with Seawater Intrusion: Macro-Hybrid Primal Mixed Variational Analysis

Macro-hybrid primal mixed variational formulations of evolution filtration problems, with seawater intrusion, are studied. This is an evolution version of our previous paper on steady macro-hybrid penalized variational problems (G. Alduncin, “Steady filtration problems with seawater intrusion: macro-hybrid primal mixed variational analysis,” Appl. Anal., vol. 88, pp. 921-936, 2009). Well-posedness analysis is performed at the continuous level via duality principles and penalization. For parallel computing, macro-hybrid primal mixed spatial decompositions are formulated and analyzed, with transmission conditions variationally dualized. In this manner, penalized pressure-velocity mixed variational formulations are considered on the basis of nonoverlapping domain decompositions, with vertical interfaces, of sections of coastal aquifers.