Abstract
AbstractMacro‐hybrid penalized finite element approximations are studied for steady filtration problems with seawater intrusion. On the basis of nonoverlapping domain decompositions with vertical interfaces, sections of coastal aquifers are decomposed into subsystems with simpler geometries and small scales, interconnected via transmission conditions of pressure and flux continuity. Corresponding local penalized formulations are derived from the global penalized variational formulation of the two‐free boundary flow problem, with continuity transmission conditions modelled variationally in a dual sense. Then, macro‐hybrid finite element approximations are derived for the system, defined on independent subdomain grids. Parallel relaxation penalty‐duality algorithms are proposed from fixed‐point problem characterizations. Numerical experiments exemplify the macro‐hybrid penalized theory, showing a good agreement with previous primal conforming penalized finite element approximations (Comput. Methods Appl. Mech. Engng. 2000; 190:609–624). Copyright © 2005 John Wiley & Sons, Ltd.
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