Mathématiques et Applications

The Gradient Discretisation Method

Authors: Droniou, J., Eymard, R., Gallouët, T., Guichard, C., Herbin, R.

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  • Includes a complete convergence analysis of schemes for linear and non-linear PDEs, covering all standard boundary conditions for elliptic and parabolic models
  • Presents a unified analysis of many classical, and less classical, numerical methods, including an analysis of degenerate models
  • Provides very generic compactness results for stationary and time-dependent problems
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  • ISBN 978-3-319-79042-8
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Softcover 51,99 €
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  • ISBN 978-3-319-79041-1
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About this Textbook

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.


About the authors

Jérôme Droniou is Associate Professor at Monash University, Australia. His research focuses on elliptic and parabolic PDEs. He has published many papers on theoretical and numerical analysis of models with singularities or degeneracies, including convergence analysis of schemes without regularity assumptions on the data or solutions.

Robert Eymard is professor of mathematics at Université Paris-Est Marne-la-Vallée. His research concerns  the design and analysis of numerical methods, mainly applied to fluid flows in porous media and incompressible Navier-Stokes equations.

Thierry Gallouet is  professor at the University of Aix-Marseille. His research focuses on the analysis of partial differential equations and the approximation of their solutions by numerical schemes. 

Cindy Guichard is assistant professor at Sorbonne Université. Her research is mainly focused on numerical methods for nonlinear fluid flows problems,  including  coupled  elliptic or parabolic equations  and  hyperbolic equations. 

Raphaèle Herbin is professor at the University of Aix-Marseille. She is a specialist of numerical schemes for partial differential equations, with application to incompressible and compressible fluid flows.

Table of contents (14 chapters)

  • Motivation and Basic Ideas

    Droniou, Jérôme (et al.)

    Pages 3-16

    Preview Buy Chapter 30,19 €
  • Dirichlet Boundary Conditions

    Droniou, Jérôme (et al.)

    Pages 17-65

    Preview Buy Chapter 30,19 €
  • Neumann, Fourier and Mixed Boundary Conditions

    Droniou, Jérôme (et al.)

    Pages 67-97

    Preview Buy Chapter 30,19 €
  • Time-Dependent GDM

    Droniou, Jérôme (et al.)

    Pages 101-121

    Preview Buy Chapter 30,19 €
  • Non Degenerate Parabolic Problems

    Droniou, Jérôme (et al.)

    Pages 123-166

    Preview Buy Chapter 30,19 €

Buy this book

eBook 41,64 €
price for Spain (gross)
  • ISBN 978-3-319-79042-8
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover 51,99 €
price for Spain (gross)
  • ISBN 978-3-319-79041-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
The Gradient Discretisation Method
Authors
Series Title
Mathématiques et Applications
Series Volume
82
Copyright
2018
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing AG, part of Springer Nature
eBook ISBN
978-3-319-79042-8
DOI
10.1007/978-3-319-79042-8
Softcover ISBN
978-3-319-79041-1
Series ISSN
1154-483X
Edition Number
1
Number of Pages
XXIV, 497
Number of Illustrations
19 b/w illustrations, 14 illustrations in colour
Topics