The Gradient Discretisation Method

Jerome Droniou, Robert Eymard, Thierry Gallouet, Cindy Guichard, Raphaèle Herbin

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Abstract

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.
Original languageEnglish
Place of PublicationCham Switzerland
PublisherSpringer
Number of pages497
Volume82
ISBN (Electronic)9783319790428
ISBN (Print)9783319790411
DOIs
Publication statusPublished - 2018

Publication series

NameMathématiques et Applications
PublisherSpringer
Volume82
ISSN (Print)1154-483X
ISSN (Electronic)2198-3275

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