An Introduction to the Gradient Discretisation Method

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

doi:10.1007/978-3-319-96415-7_40

An Introduction to the Gradient Discretisation Method

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

School of Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Conference Paper › Research › peer-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 language	English
Title of host publication	Numerical Mathematics and Advanced Applications ENUMATH 2017
Editors	Florin Adrian Radu, Kundan Kumar, Inga Berre, Jan Martin Nordbotten, Iuliu Sorin Pop
Publisher	Springer
Pages	451-459
Number of pages	9
Volume	126
ISBN (Electronic)	9783319964157
ISBN (Print)	9783319964140
DOIs	https://doi.org/10.1007/978-3-319-96415-7_40
Publication status	Published - 1 Jan 2019
Event	European Conference on Numerical Mathematics and Advanced Applications 2017 - Voss, Norway Duration: 25 Sep 2017 → 29 Sep 2017 https://link.springer.com/book/10.1007%2F978-3-319-96415-7 (Proceedings)

Publication series

Name	Lecture Notes in Computational Science and Engineering
Volume	126
ISSN (Print)	1439-7358
ISSN (Electronic)	2197-7100

Conference

Conference	European Conference on Numerical Mathematics and Advanced Applications 2017
Abbreviated title	ENUMATH 2017
Country	Norway
City	Voss
Period	25/09/17 → 29/09/17
Internet address	https://link.springer.com/book/10.1007%2F978-3-319-96415-7 (Proceedings)

Access to Document

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

Link to publication in Scopus

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).

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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 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 proceeding › Conference Paper › Research › peer-review

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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