# The G method for heterogeneous anisotropic diffusion on general meshes

Léo Agélas; Daniele A. Di Pietro; Jérôme Droniou

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

- Volume: 44, Issue: 4, page 597-625
- ISSN: 0764-583X

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topAgélas, Léo, Di Pietro, Daniele A., and Droniou, Jérôme. "The G method for heterogeneous anisotropic diffusion on general meshes." ESAIM: Mathematical Modelling and Numerical Analysis 44.4 (2010): 597-625. <http://eudml.org/doc/250781>.

@article{Agélas2010,

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
$H_0^1$(Ω) 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 = {Agélas, Léo, Di Pietro, Daniele A., Droniou, Jérôme},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

keywords = {Finite volume methods; heterogeneous anisotropic
diffusion; MPFA; convergence analysis; cell centered finite volume scheme; heterogeneous anisotropic diffusion; comparison of methods; anisotropic elliptic problems; MPFA methods},

language = {eng},

month = {6},

number = {4},

pages = {597-625},

publisher = {EDP Sciences},

title = {The G method for heterogeneous anisotropic diffusion on general meshes},

url = {http://eudml.org/doc/250781},

volume = {44},

year = {2010},

}

TY - JOUR

AU - Agélas, Léo

AU - Di Pietro, Daniele A.

AU - Droniou, Jérôme

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

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2010/6//

PB - EDP Sciences

VL - 44

IS - 4

SP - 597

EP - 625

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
$H_0^1$(Ω) 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.

LA - eng

KW - Finite volume methods; heterogeneous anisotropic
diffusion; MPFA; convergence analysis; cell centered finite volume scheme; heterogeneous anisotropic diffusion; comparison of methods; anisotropic elliptic problems; MPFA methods

UR - http://eudml.org/doc/250781

ER -

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