An Introduction to the Gradient Discretisation Method

Jérôme Droniou, Robert Eymard, Thierry Gallouët, Cindy Guichard, Raphaèle Herbin

Research output: Chapter in Book/Report/Conference proceedingConference PaperResearchpeer-review

Abstract

We show that three classical examples of schemes for the approximation of linear elliptic problems can be cast in a common framework, called the gradient discretisation method (GDM). An error estimate is then obtained by the extension to this framework of the second Strang lemma, which is completed by a second inequality showing that the conditions which are sufficient for the convergence of the method are also necessary.

Original languageEnglish
Title of host publicationNumerical Mathematics and Advanced Applications ENUMATH 2017
EditorsFlorin Adrian Radu, Kundan Kumar, Inga Berre, Jan Martin Nordbotten, Iuliu Sorin Pop
PublisherSpringer
Pages451-459
Number of pages9
Volume126
ISBN (Electronic)9783319964157
ISBN (Print)9783319964140
DOIs
Publication statusPublished - 1 Jan 2019
EventEuropean Conference on Numerical Mathematics and Advanced Applications, ENUMATH 2017 - Voss, Norway
Duration: 25 Sep 201729 Sep 2017

Publication series

NameLecture Notes in Computational Science and Engineering
Volume126
ISSN (Print)1439-7358
ISSN (Electronic)2197-7100

Conference

ConferenceEuropean Conference on Numerical Mathematics and Advanced Applications, ENUMATH 2017
CountryNorway
CityVoss
Period25/09/1729/09/17

Cite this

Droniou, J., Eymard, R., Gallouët, T., Guichard, C., & Herbin, R. (2019). An Introduction to the Gradient Discretisation Method. In F. A. Radu, K. Kumar, I. Berre, J. M. Nordbotten, & I. S. Pop (Eds.), Numerical Mathematics and Advanced Applications ENUMATH 2017 (Vol. 126, pp. 451-459). (Lecture Notes in Computational Science and Engineering; Vol. 126). Springer. https://doi.org/10.1007/978-3-319-96415-7_40
Droniou, Jérôme ; Eymard, Robert ; Gallouët, Thierry ; Guichard, Cindy ; Herbin, Raphaèle. / An Introduction to the Gradient Discretisation Method. Numerical Mathematics and Advanced Applications ENUMATH 2017. editor / Florin Adrian Radu ; Kundan Kumar ; Inga Berre ; Jan Martin Nordbotten ; Iuliu Sorin Pop. Vol. 126 Springer, 2019. pp. 451-459 (Lecture Notes in Computational Science and Engineering).
@inproceedings{8f32e9e018754e889b7596eb3e8cdcbe,
title = "An Introduction to the Gradient Discretisation Method",
abstract = "We show that three classical examples of schemes for the approximation of linear elliptic problems can be cast in a common framework, called the gradient discretisation method (GDM). An error estimate is then obtained by the extension to this framework of the second Strang lemma, which is completed by a second inequality showing that the conditions which are sufficient for the convergence of the method are also necessary.",
author = "J{\'e}r{\^o}me Droniou and Robert Eymard and Thierry Gallou{\"e}t and Cindy Guichard and Rapha{\`e}le Herbin",
year = "2019",
month = "1",
day = "1",
doi = "10.1007/978-3-319-96415-7_40",
language = "English",
isbn = "9783319964140",
volume = "126",
series = "Lecture Notes in Computational Science and Engineering",
publisher = "Springer",
pages = "451--459",
editor = "Radu, {Florin Adrian} and Kundan Kumar and Inga Berre and Nordbotten, {Jan Martin} and Pop, {Iuliu Sorin}",
booktitle = "Numerical Mathematics and Advanced Applications ENUMATH 2017",

}

Droniou, J, Eymard, R, Gallouët, T, Guichard, C & Herbin, R 2019, An Introduction to the Gradient Discretisation Method. in FA Radu, K Kumar, I Berre, JM Nordbotten & IS Pop (eds), Numerical Mathematics and Advanced Applications ENUMATH 2017. vol. 126, Lecture Notes in Computational Science and Engineering, vol. 126, Springer, pp. 451-459, European Conference on Numerical Mathematics and Advanced Applications, ENUMATH 2017, Voss, Norway, 25/09/17. https://doi.org/10.1007/978-3-319-96415-7_40

An Introduction to the Gradient Discretisation Method. / Droniou, Jérôme; Eymard, Robert; Gallouët, Thierry; Guichard, Cindy; Herbin, Raphaèle.

Numerical Mathematics and Advanced Applications ENUMATH 2017. ed. / Florin Adrian Radu; Kundan Kumar; Inga Berre; Jan Martin Nordbotten; Iuliu Sorin Pop. Vol. 126 Springer, 2019. p. 451-459 (Lecture Notes in Computational Science and Engineering; Vol. 126).

Research output: Chapter in Book/Report/Conference proceedingConference PaperResearchpeer-review

TY - GEN

T1 - An Introduction to the Gradient Discretisation Method

AU - Droniou, Jérôme

AU - Eymard, Robert

AU - Gallouët, Thierry

AU - Guichard, Cindy

AU - Herbin, Raphaèle

PY - 2019/1/1

Y1 - 2019/1/1

N2 - We show that three classical examples of schemes for the approximation of linear elliptic problems can be cast in a common framework, called the gradient discretisation method (GDM). An error estimate is then obtained by the extension to this framework of the second Strang lemma, which is completed by a second inequality showing that the conditions which are sufficient for the convergence of the method are also necessary.

AB - We show that three classical examples of schemes for the approximation of linear elliptic problems can be cast in a common framework, called the gradient discretisation method (GDM). An error estimate is then obtained by the extension to this framework of the second Strang lemma, which is completed by a second inequality showing that the conditions which are sufficient for the convergence of the method are also necessary.

UR - http://www.scopus.com/inward/record.url?scp=85060058802&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-96415-7_40

DO - 10.1007/978-3-319-96415-7_40

M3 - Conference Paper

SN - 9783319964140

VL - 126

T3 - Lecture Notes in Computational Science and Engineering

SP - 451

EP - 459

BT - Numerical Mathematics and Advanced Applications ENUMATH 2017

A2 - Radu, Florin Adrian

A2 - Kumar, Kundan

A2 - Berre, Inga

A2 - Nordbotten, Jan Martin

A2 - Pop, Iuliu Sorin

PB - Springer

ER -

Droniou J, Eymard R, Gallouët T, Guichard C, Herbin R. An Introduction to the Gradient Discretisation Method. In Radu FA, Kumar K, Berre I, Nordbotten JM, Pop IS, editors, Numerical Mathematics and Advanced Applications ENUMATH 2017. Vol. 126. Springer. 2019. p. 451-459. (Lecture Notes in Computational Science and Engineering). https://doi.org/10.1007/978-3-319-96415-7_40