An Introduction to the Gradient Discretisation Method

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

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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