Gradient schemes: Generic tools for the numerical analysis of diffusion equations

Jerome Droniou, Robert Eymard, Raphaèle Herbin

Research output: Contribution to journalArticleResearchpeer-review

33 Citations (Scopus)

Abstract

The gradient scheme framework is based on a small number of properties and encompasses a large number of numerical methods for diffusion models. We recall these properties and develop some new generic tools associated with the gradient scheme framework. These tools enable us to prove that classical schemes are indeed gradient schemes, and allow us to perform a complete and generic study of the well-known (but rarely well-studied) mass lumping process. They also allow an easy check of the mathematical properties of new schemes, by developing a generic process for eliminating unknowns via barycentric condensation, and by designing a concept of discrete functional analysis toolbox for schemes based on polytopal meshes.

Original languageEnglish
Pages (from-to)749-781
Number of pages33
JournalEsaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique
Volume50
Issue number3
DOIs
Publication statusPublished - 1 May 2016

Keywords

  • Convergence analysis
  • Diffusion equations
  • Discrete functional analysis
  • Gradient discretisation
  • Gradient scheme
  • Numerical scheme

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