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The Rain on Underground Porous Media

In: Partial Differential Equations: Theory, Control and Approximation

Author

Listed:
  • 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))

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.

Suggested Citation

  • Christine Bernardi & Adel Blouza & Linda El Alaoui, 2014. "The Rain on Underground Porous Media," Springer Books, in: Philippe G. Ciarlet & Tatsien Li & Yvon Maday (ed.), Partial Differential Equations: Theory, Control and Approximation, edition 127, pages 41-66, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-41401-5_2
    DOI: 10.1007/978-3-642-41401-5_2
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