The Gradient Discretisation Method

Jerome Droniou, Robert Eymard, Thierry Gallouet, Cindy Guichard, Raphaèle Herbin

Research output: Book/ReportBookResearchpeer-review

Abstract

This monograph presents the Gradient Discretisation Method (GDM), which is a unified convergence analysis framework for numerical methods for elliptic and parabolic partial differential equations. The results obtained by the GDM cover both stationary and transient models; error estimates are provided for linear (and some non-linear) equations, and convergence is established for a wide range of fully non-linear models (e.g. Leray–Lions equations and degenerate parabolic equations such as the Stefan or Richards models). The GDM applies to a diverse range of methods, both classical (conforming, non-conforming, mixed finite elements, discontinuous Galerkin) and modern (mimetic finite differences, hybrid and mixed finite volume, MPFA-O finite volume), some of which can be built on very general meshes.
Original languageEnglish
Place of PublicationCham Switzerland
PublisherSpringer
Number of pages497
Volume82
ISBN (Electronic)9783319790428
ISBN (Print)9783319790411
DOIs
Publication statusPublished - 2018

Publication series

NameMathématiques et Applications
PublisherSpringer
Volume82
ISSN (Print)1154-483X
ISSN (Electronic)2198-3275

Cite this

Droniou, J., Eymard, R., Gallouet, T., Guichard, C., & Herbin, R. (2018). The Gradient Discretisation Method. (Mathématiques et Applications; Vol. 82). Cham Switzerland: Springer. https://doi.org/10.1007/978-3-319-79042-8
Droniou, Jerome ; Eymard, Robert ; Gallouet, Thierry ; Guichard, Cindy ; Herbin, Raphaèle. / The Gradient Discretisation Method. Cham Switzerland : Springer, 2018. 497 p. (Mathématiques et Applications).
@book{129fd7b6eb6c4b859e4ef1f3b041d86f,
title = "The Gradient Discretisation Method",
abstract = "This monograph presents the Gradient Discretisation Method (GDM), which is a unified convergence analysis framework for numerical methods for elliptic and parabolic partial differential equations. The results obtained by the GDM cover both stationary and transient models; error estimates are provided for linear (and some non-linear) equations, and convergence is established for a wide range of fully non-linear models (e.g. Leray–Lions equations and degenerate parabolic equations such as the Stefan or Richards models). The GDM applies to a diverse range of methods, both classical (conforming, non-conforming, mixed finite elements, discontinuous Galerkin) and modern (mimetic finite differences, hybrid and mixed finite volume, MPFA-O finite volume), some of which can be built on very general meshes.",
author = "Jerome Droniou and Robert Eymard and Thierry Gallouet and Cindy Guichard and Rapha{\`e}le Herbin",
year = "2018",
doi = "10.1007/978-3-319-79042-8",
language = "English",
isbn = "9783319790411",
volume = "82",
series = "Math{\'e}matiques et Applications",
publisher = "Springer",

}

Droniou, J, Eymard, R, Gallouet, T, Guichard, C & Herbin, R 2018, The Gradient Discretisation Method. Mathématiques et Applications, vol. 82, vol. 82, Springer, Cham Switzerland. https://doi.org/10.1007/978-3-319-79042-8

The Gradient Discretisation Method. / Droniou, Jerome; Eymard, Robert; Gallouet, Thierry; Guichard, Cindy; Herbin, Raphaèle.

Cham Switzerland : Springer, 2018. 497 p. (Mathématiques et Applications; Vol. 82).

Research output: Book/ReportBookResearchpeer-review

TY - BOOK

T1 - The Gradient Discretisation Method

AU - Droniou, Jerome

AU - Eymard, Robert

AU - Gallouet, Thierry

AU - Guichard, Cindy

AU - Herbin, Raphaèle

PY - 2018

Y1 - 2018

N2 - This monograph presents the Gradient Discretisation Method (GDM), which is a unified convergence analysis framework for numerical methods for elliptic and parabolic partial differential equations. The results obtained by the GDM cover both stationary and transient models; error estimates are provided for linear (and some non-linear) equations, and convergence is established for a wide range of fully non-linear models (e.g. Leray–Lions equations and degenerate parabolic equations such as the Stefan or Richards models). The GDM applies to a diverse range of methods, both classical (conforming, non-conforming, mixed finite elements, discontinuous Galerkin) and modern (mimetic finite differences, hybrid and mixed finite volume, MPFA-O finite volume), some of which can be built on very general meshes.

AB - This monograph presents the Gradient Discretisation Method (GDM), which is a unified convergence analysis framework for numerical methods for elliptic and parabolic partial differential equations. The results obtained by the GDM cover both stationary and transient models; error estimates are provided for linear (and some non-linear) equations, and convergence is established for a wide range of fully non-linear models (e.g. Leray–Lions equations and degenerate parabolic equations such as the Stefan or Richards models). The GDM applies to a diverse range of methods, both classical (conforming, non-conforming, mixed finite elements, discontinuous Galerkin) and modern (mimetic finite differences, hybrid and mixed finite volume, MPFA-O finite volume), some of which can be built on very general meshes.

U2 - 10.1007/978-3-319-79042-8

DO - 10.1007/978-3-319-79042-8

M3 - Book

SN - 9783319790411

VL - 82

T3 - Mathématiques et Applications

BT - The Gradient Discretisation Method

PB - Springer

CY - Cham Switzerland

ER -

Droniou J, Eymard R, Gallouet T, Guichard C, Herbin R. The Gradient Discretisation Method. Cham Switzerland: Springer, 2018. 497 p. (Mathématiques et Applications). https://doi.org/10.1007/978-3-319-79042-8