Mathématiques et Applications

Droniou, Jérôme; Eymard, Robert; Gallouët, Thierry; Guichard, Cindy; Herbin, Raphaèle

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.

Details

Published by: Springer

Publication Date: 2018-08-11

Format: Paperback

ISBN-13: 9783319790411

DOI: 10.1007/978-3-319-79042-8

Dimensions: 235cm x155cm

Pages: 497