The gradient discretisation method
type: Item
instance of: scholarly article
title: The gradient discretisation method
zbMATH Open document ID: 1435.65005
DOI: 10.1007/978-3-319-79042-8
author: Jérôme Droniou
author: Cindy Guichard
author: Raphaèle Herbin
author: Robert Eymard
author: T. Gallouët
published in: Mathématiques \& Applications (Berlin)
publication date: 2018-06-29T00:00:00Z
review text: This monograph focuses on the Gradient Discretisation Method, which is introduced as a unified convergence analysis framework for numerical methods for elliptic and parabolic partial differential equations. Several examples of numerical methods are shown to fall into the range of the discrete gradient discretization methods: The GDM applies e.g. to both classical (conforming, non-conforming, mixed finite elements, discontinuous Galerkin) and modern (mimetic finite differences, hybrid and mixed finite volume) discretization methods. The convergence results are obtained by the GDM for both stationary and transient models. An error estimates are provided for linear equations, and several nonlinear equations are investigated as well. The convergence is established for a wide range of fully non-linear models as Leray-Lions equations and degenerate parabolic equations such as the Stefan or Richards model.
reviewed by: Petr Sváček
Mathematics Subject Classification ID: 65-02
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 65M15
Mathematics Subject Classification ID: 65M60
Mathematics Subject Classification ID: 65N12
Mathematics Subject Classification ID: 65N15
Mathematics Subject Classification ID: 65N30
zbMATH DE Number: 6897811
zbMATH Keywords: gradient discretisation method
zbMATH Keywords: gradient schemes
zbMATH Keywords: elliptic partial differential equations
zbMATH Keywords: parabolic partial differential equations
zbMATH Keywords: unified convergence analysis
zbMATH Keywords: discrete Aubin-Simon compactness theorems
zbMATH Keywords: convergence by compactness
zbMATH Keywords: error estimates
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/978-3-319-79042-8
OpenAlex ID: W4205793979
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description: scientific article; zbMATH DE number 6897811