Abstract
| Original language | English |
|---|---|
| Place of Publication | Cham Switzerland |
| Publisher | Springer |
| Number of pages | 497 |
| Volume | 82 |
| ISBN (Electronic) | 9783319790428 |
| ISBN (Print) | 9783319790411 |
| DOIs | |
| Publication status | Published - 2018 |
Publication series
| Name | Mathématiques et Applications |
|---|---|
| Publisher | Springer |
| Volume | 82 |
| ISSN (Print) | 1154-483X |
| ISSN (Electronic) | 2198-3275 |
Cite this
}
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/Report › Book › Research › peer-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 -