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An Introduction to the Gradient Discretisation Method

  • Jérôme Droniou
  • Robert Eymard
  • Thierry Gallouët
  • Cindy Guichard
  • Raphaèle HerbinEmail author
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 126)

Abstract

We show that three classical examples of schemes for the approximation of linear elliptic problems can be cast in a common framework, called the gradient discretisation method (GDM). An error estimate is then obtained by the extension to this framework of the second Strang lemma, which is completed by a second inequality showing that the conditions which are sufficient for the convergence of the method are also necessary.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Jérôme Droniou
    • 1
  • Robert Eymard
    • 2
  • Thierry Gallouët
    • 3
  • Cindy Guichard
    • 4
  • Raphaèle Herbin
    • 3
    Email author
  1. 1.School of Mathematical SciencesMonash UniversityClaytonAustralia
  2. 2.Université Paris-EstLAMA (UMR 8050), UPEM, UPEC, CNRSMarne-la-ValléeFrance
  3. 3.Aix Marseille UniversitéCNRS, Centrale Marseille, I2MMarseilleFrance
  4. 4.Sorbonne UniversitésUPMC Univ Paris 06, CNRS, UMR 7598, LJLLParisFrance

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