The gradient discretisation method
著者
書誌事項
The gradient discretisation method
（Mathématiques & applications / directeurs de la collection, J.M. Ghidaglia et P. Lascaux, 82）
Springer, c2018
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注記
Other authors: Robert Eymard, Thierry Gallouët, Cindy Guichard, Raphaèle Herbin
Includes bibliographical references (p. 487-493) and index
内容説明・目次
内容説明
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.
目次
Part I Elliptic problems.- Part II Parabolic problems.- Part III Examples of gradient discretisation methods.- Part IV Appendix.
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