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

Jerome Droniou

doi:10.1051/m2an:2007001

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

Jerome Droniou

Research output: Contribution to journal › Article › Research › peer-review

25 Citations (Scopus)

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 language	English
Pages (from-to)	1069-1100
Number of pages	32
Journal	Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique
Volume	40
Issue number	6
DOIs	https://doi.org/10.1051/m2an:2007001
Publication status	Published - 1 Nov 2006
Externally published	Yes

Keywords

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

Access to Document

10.1051/m2an:2007001

32314716-oaFinal published version, 372 KB

Link to publication in Scopus

Cite this

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KW - Non-linear elliptic equations

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