The Gradient Discretisation Method
Springer International Publishing (Verlag)
978-3-319-79041-1 (ISBN)
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.
Jérôme Droniou is Associate Professor at Monash University
Part I Elliptic problems.- Part II Parabolic problems.- Part III Examples of gradient discretisation methods.- Part IV Appendix.
| Erscheinungsdatum | 12.08.2018 |
|---|---|
| Reihe/Serie | Mathématiques et Applications |
| Zusatzinfo | XXIV, 497 p. 33 illus., 14 illus. in color. |
| Verlagsort | Cham |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Gewicht | 795 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik | |
| Schlagworte | Convergence by compactness • Discrete Aubin-Simon compactness theorems • Elliptic Partial Differential Equations • error estimates • Gradient Discretisation Method • Gradient schemes • Parabolic partial differential equations • Partial differential equations • Unified convergence analysis |
| ISBN-10 | 3-319-79041-2 / 3319790412 |
| ISBN-13 | 978-3-319-79041-1 / 9783319790411 |
| Zustand | Neuware |
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