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The Rain on Underground Porous Media

Part I: Analysis of a Richards Model
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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 

Mathematics Subject Classification

76S05 76M10 65M12 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Laboratoire Jacques-Louis LionsCNRS & Université Pierre et Marie CurieParis Cedex 05France
  2. 2.Laboratoire de Mathématiques Raphaël Salem (UMR 6085 CNRS)Université de Rouen, Avenue de l’UniversitéSaint-Étienne-du-RouvrayFrance
  3. 3.University Paris 13, Sorbonne Paris City, LAGA, CNRS (UMR 7539)VilletaneuseFrance

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