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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.

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Authors and Affiliations

  1. Laboratoire Jacques-Louis Lions, CNRS & Université Pierre et Marie Curie, BC 187, 4 Place Jussieu, 75252, Paris Cedex 05, France

    Christine Bernardi

  2. Laboratoire de Mathématiques Raphaël Salem (UMR 6085 CNRS), Université de Rouen, Avenue de l’Université, BP 12, 76801, Saint-Étienne-du-Rouvray, France

    Adel Blouza

  3. Sorbonne Paris Cit, LAGA, CNRS (UMR 7539), Universit Paris 13, F-93430, Villetaneuse, France

    Linda El Alaoui

Authors
  1. Christine Bernardi
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  2. Adel Blouza
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  3. Linda El Alaoui
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Correspondence to Christine Bernardi.

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In honor of the scientific heritage of Jacques-Louis Lions

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Bernardi, C., Blouza, A. & El Alaoui, L. The rain on underground porous media Part I: Analysis of a richards model. Chin. Ann. Math. Ser. B 34, 193–212 (2013). https://doi.org/10.1007/s11401-013-0766-z

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  • DOI: https://doi.org/10.1007/s11401-013-0766-z

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