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

Jerome Droniou

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18 Citations (Scopus)


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
Issue number6
Publication statusPublished - 1 Nov 2006
Externally publishedYes


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

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