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Uniform-in-Time Convergence of Numerical Schemes for Richards’ and Stefan’s Models

  • Jérôme Droniou
  • Robert Eymard
  • Cindy Guichard
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 77)

Abstract

We prove that all Gradient Schemes—which include Finite Element, Mixed Finite Element, Finite Volume methods—converge uniformly in time when applied to a family of nonlinear parabolic equations which contains Richards and Stefan’s models. We also provide numerical results to confirm our theoretical analysis.

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Jérôme Droniou
    • 1
  • Robert Eymard
    • 2
  • Cindy Guichard
    • 3
  1. 1.School of Mathematical SciencesMonash UniversityVictoriaAustralia
  2. 2.Laboratoire d’Analyse et de Mathématiques AppliquéesCNRS, UPEM, UPEC, 5 boulevard Descartes, Champs-sur-MarneMarne-la-Vallée Cedex 2France
  3. 3.Laboratoire Jacques-Louis LionsSorbonne Universités, UPMC Univ Paris 06, UMR 7598ParisFrance

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