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Steady filtration with seawater intrusion: Penalized finite element approximations. (English) Zbl 1006.76049

From the summary: 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 allows to formulate this two-free boundary problem in terms of a nonsubdifferential inequality. We prove the convergence of conforming finite element approximations, and for numerical stabilization, we apply the Tabata upwind technique. For resolution purposes, the resulting discrete nonlinear penalized model is reduced to a fixed-point problem, which is solved by an iterative algorithm. Finally, some numerical applications exemplify the theory.

MSC:

76M10 Finite element methods applied to problems in fluid mechanics
76S05 Flows in porous media; filtration; seepage
86A05 Hydrology, hydrography, oceanography

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References:

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