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

Research output: Contribution to journalArticleResearchpeer-review

22 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 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

Cite this

@article{38da3a3012e741aebe07b150b422a5f8,
title = "Finite volume schemes for fully non-linear elliptic equations in divergence form",
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.",
keywords = "Finite volume schemes, Irregular grids, Leray-Lions operators, Non-linear elliptic equations",
author = "Jerome Droniou",
year = "2006",
month = "11",
day = "1",
doi = "10.1051/m2an:2007001",
language = "English",
volume = "40",
pages = "1069--1100",
journal = "Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique",
issn = "0764-583X",
publisher = "EDP Sciences",
number = "6",

}

Finite volume schemes for fully non-linear elliptic equations in divergence form. / Droniou, Jerome.

In: Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique, Vol. 40, No. 6, 01.11.2006, p. 1069-1100.

Research output: Contribution to journalArticleResearchpeer-review

TY - JOUR

T1 - Finite volume schemes for fully non-linear elliptic equations in divergence form

AU - Droniou, Jerome

PY - 2006/11/1

Y1 - 2006/11/1

N2 - 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.

AB - 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.

KW - Finite volume schemes

KW - Irregular grids

KW - Leray-Lions operators

KW - Non-linear elliptic equations

UR - http://www.scopus.com/inward/record.url?scp=33847227277&partnerID=8YFLogxK

U2 - 10.1051/m2an:2007001

DO - 10.1051/m2an:2007001

M3 - Article

VL - 40

SP - 1069

EP - 1100

JO - Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique

JF - Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique

SN - 0764-583X

IS - 6

ER -