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

34 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
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

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 = nov,

day = "1",

doi = "10.1051/m2an:2007001",

language = "English",

volume = "40",

pages = "1069--1100",

journal = "ESAIM: Mathematical Modelling and Numerical Analysis",

issn = "0764-583X",

publisher = "EDP Sciences",

number = "6",

}

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

AN - SCOPUS:33847227277

SN - 0764-583X

VL - 40

SP - 1069

EP - 1100

JO - ESAIM: Mathematical Modelling and Numerical Analysis

JF - ESAIM: Mathematical Modelling and Numerical Analysis

IS - 6

ER -

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

Abstract

Keywords

Access to Document

Other files and links

Cite this