Steady filtration problems with seawater intrusion: macro-hybrid primal mixed variational analysis

Abstract

Macro-hybrid penalized, primal mixed continuous and discrete variational formulations, for steady filtration problems, with seawater intrusion, are studied. This is a mixed version of our previous paper on macro-hybrid penalized approximations (G. Alduncin, J. Esquivel-Avila, and N. Vera-Guzman, Steady filtration problems with seawater intrusion: Macro-hybrid penalized finite element approximations, Int. J. Numer. Meth. Fluids (2005) 49, pp. 935–957). Penalized pressure–velocity mixed variational formulations are introduced for non-overlapping domain decompositions, with vertical interfaces, of sections of coastal aquifers. Well-posedness and stability conditions are established at the continuous and discrete levels. Macro-hybrid primal mixed internal approximations are defined on independent subdomain grids, with transmission conditions imposed in a dual variational sense. Parallel relaxation penalty-duality algorithms are discussed from fixed-point characterizations, for iterative numerical resolution.

Keywords:

• open flow in porous media
• seawater intrusion
• two-free boundary problem
• hybrid domain decomposition method
• internal primal mixed variational discretization
• relaxation proximal-point algorithm

AMS Subject Classifications::

• 76S05
• 49J40
• 65Y06
• 35R35