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The Gradient Discretisation Method

The Gradient Discretisation Method

Paperback

Series: Mathématiques Et Applications, Book 82

General Mathematics

ISBN10: 3319790412
ISBN13: 9783319790411
Publisher: Springer
Published: Aug 11 2018
Pages: 497
Weight: 1.60
Height: 1.05 Width: 6.14 Depth: 9.21
Language: English

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.


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General Mathematics