The Gradient Discretisation Method

By Robert Eymard, Thierry Gallouët, Jérôme Droniou

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.

• Format: Paperback
• Language: English
• ISBN: 3319790412
• ISBN13: 9783319790411
• Release Date: August 2018
• Publisher: Springer
• Length: 497 Pages
• Weight: 1.60 lbs.
• Dimensions: 1.1" x 6.1" x 9.2"