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.
| Autorius: | Jérôme Droniou, Robert Eymard, Raphaèle Herbin, Cindy Guichard, Thierry Gallouët, |
| Serija: | Mathématiques et Applications |
| Leidėjas: | Springer Nature Switzerland |
| Išleidimo metai: | 2018 |
| Knygos puslapių skaičius: | 524 |
| ISBN-10: | 3319790412 |
| ISBN-13: | 9783319790411 |
| Formatas: | Knyga minkštu viršeliu |
| Kalba: | Anglų |
| Žanras: | Differential calculus and equations |
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