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 | |
| Publication status | Published - 1 Jan 2019 |
| Event | European Conference on Numerical Mathematics and Advanced Applications, ENUMATH 2017 - Voss, Norway Duration: 25 Sep 2017 → 29 Sep 2017 |
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, ENUMATH 2017 |
|---|---|
| Country | Norway |
| City | Voss |
| Period | 25/09/17 → 29/09/17 |
Cite this
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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
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 -