Finite volume schemes for fully non-linear elliptic equations in divergence form

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Abstract

We construct finite volume schemes, on unstructured and irregular grids and in any space dimension, for non-linear elliptic equations of the p-Laplacian kind: -div(|∇u|p-2∇u) = f (with 1 < p < ∞). We prove the existence and uniqueness of the approximate solutions, as well as their strong convergence towards the solution of the PDE. The outcome of some numerical tests are also provided.

Original languageEnglish
Pages (from-to)1069-1100
Number of pages32
JournalEsaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique
Volume40
Issue number6
DOIs
Publication statusPublished - 1 Nov 2006
Externally publishedYes

Keywords

  • Finite volume schemes
  • Irregular grids
  • Leray-Lions operators
  • Non-linear elliptic equations

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