The Rain on Underground Porous Media

Christine Bernardi (), Adel Blouza () and Linda El Alaoui ()
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Christine Bernardi: CNRS & Université Pierre et Marie Curie, Laboratoire Jacques-Louis Lions
Adel Blouza: Université de Rouen, Avenue de l’Université, Laboratoire de Mathématiques Raphaël Salem (UMR 6085 CNRS)
Linda El Alaoui: University Paris 13, Sorbonne Paris City, LAGA, CNRS (UMR 7539)

A chapter in Partial Differential Equations: Theory, Control and Approximation, 2014, pp 41-66 from Springer

Abstract: Abstract The Richards equation models the water flow in a partially saturated underground porous medium under the surface. When it rains on the surface, boundary conditions of Signorini type must be considered on this part of the boundary. The authors first study this problem which results into a variational inequality and then propose a discretization by an implicit Euler’s scheme in time and finite elements in space. The convergence of this discretization leads to the well-posedness of the problem.

Keywords: Richards equation; Porous media; Euler’s implicit scheme; Finite element discretization; Parabolic variational inequality; 76S05; 76M10; 65M12 (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-41401-5_2

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DOI: 10.1007/978-3-642-41401-5_2

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