The Gradient Discretisation Method (Mathématiques et Applications) （2018）

Droniou, Jérôme/ Eymard, Robert/ Gallouët, Thierry

Springer International Publishing AG（2018/08発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 497 p.
• 言語 ENG
• 商品コード 9783319790411
• DDC分類 515.353

Full Description

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.

Contents

Part I Elliptic problems.- Part II Parabolic problems.- Part III Examples of gradient discretisation methods.- Part IV Appendix.