The G method for heterogeneous anisotropic diffusion on general meshes

Leo Agelas, Daniele A Di Pietro, Jerome Droniou

Research output: Contribution to journalArticleResearchpeer-review

31 Citations (Scopus)

Abstract

In the present work we introduce a new family of cell-centered Finite Volume schemes for anisotropic and heterogeneous diffusion operators inspired by the MPFA L method. A very general framework for the convergence study of finite volume methods is provided and then used to establish the convergence of the new method. Fairly general meshes are covered and a computable sufficient criterion for coercivity is provided. In order to guarantee consistency in the presence of heterogeneous diffusivity, we introduce a non-standard test space in H(0)(1)(Omega) and prove its density. Thorough assessment on a set of anisotropic heterogeneous problems as well as a comparison with classical multi-point Finite Volume methods is provided.
Original languageEnglish
Pages (from-to)597 - 625
Number of pages29
JournalEsaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique
Volume44
Issue number4
DOIs
Publication statusPublished - 2010
Externally publishedYes

Cite this

@article{6a9a7a0236e3468e9daf418dde84cad4,
title = "The G method for heterogeneous anisotropic diffusion on general meshes",
abstract = "In the present work we introduce a new family of cell-centered Finite Volume schemes for anisotropic and heterogeneous diffusion operators inspired by the MPFA L method. A very general framework for the convergence study of finite volume methods is provided and then used to establish the convergence of the new method. Fairly general meshes are covered and a computable sufficient criterion for coercivity is provided. In order to guarantee consistency in the presence of heterogeneous diffusivity, we introduce a non-standard test space in H(0)(1)(Omega) and prove its density. Thorough assessment on a set of anisotropic heterogeneous problems as well as a comparison with classical multi-point Finite Volume methods is provided.",
author = "Leo Agelas and {Di Pietro}, {Daniele A} and Jerome Droniou",
year = "2010",
doi = "10.1051/m2an/2010021",
language = "English",
volume = "44",
pages = "597 -- 625",
journal = "Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique",
issn = "0764-583X",
publisher = "EDP Sciences",
number = "4",

}

The G method for heterogeneous anisotropic diffusion on general meshes. / Agelas, Leo; Di Pietro, Daniele A; Droniou, Jerome.

In: Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique, Vol. 44, No. 4, 2010, p. 597 - 625.

Research output: Contribution to journalArticleResearchpeer-review

TY - JOUR

T1 - The G method for heterogeneous anisotropic diffusion on general meshes

AU - Agelas, Leo

AU - Di Pietro, Daniele A

AU - Droniou, Jerome

PY - 2010

Y1 - 2010

N2 - In the present work we introduce a new family of cell-centered Finite Volume schemes for anisotropic and heterogeneous diffusion operators inspired by the MPFA L method. A very general framework for the convergence study of finite volume methods is provided and then used to establish the convergence of the new method. Fairly general meshes are covered and a computable sufficient criterion for coercivity is provided. In order to guarantee consistency in the presence of heterogeneous diffusivity, we introduce a non-standard test space in H(0)(1)(Omega) and prove its density. Thorough assessment on a set of anisotropic heterogeneous problems as well as a comparison with classical multi-point Finite Volume methods is provided.

AB - In the present work we introduce a new family of cell-centered Finite Volume schemes for anisotropic and heterogeneous diffusion operators inspired by the MPFA L method. A very general framework for the convergence study of finite volume methods is provided and then used to establish the convergence of the new method. Fairly general meshes are covered and a computable sufficient criterion for coercivity is provided. In order to guarantee consistency in the presence of heterogeneous diffusivity, we introduce a non-standard test space in H(0)(1)(Omega) and prove its density. Thorough assessment on a set of anisotropic heterogeneous problems as well as a comparison with classical multi-point Finite Volume methods is provided.

UR - http://www.esaim-m2an.org/action/displayAbstract?fromPage=online&aid=8133314

U2 - 10.1051/m2an/2010021

DO - 10.1051/m2an/2010021

M3 - Article

VL - 44

SP - 597

EP - 625

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 - 4

ER -