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

Abstract

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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.

How to cite

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Agélas, 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 -

References

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Citations in EuDML Documents

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  1. Daniele A. Di Pietro, Cell centered Galerkin methods for diffusive problems
  2. Daniele A. Di Pietro, Cell centered Galerkin methods for diffusive problems
  3. Mary Fanett Wheeler, Guangri Xue, Ivan Yotov, A multiscale mortar multipoint flux mixed finite element method
  4. Mary Fanett Wheeler, Guangri Xue, Ivan Yotov, A multiscale mortar multipoint flux mixed finite element method
  5. Mary Fanett Wheeler, Guangri Xue, Ivan Yotov, A multiscale mortar multipoint flux mixed finite element method

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