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SpringerBriefs in Mathematics

Error Estimates for Well-Balanced Schemes on Simple Balance Laws

One-Dimensional Position-Dependent Models

Authors: Amadori, Debora, Gosse, Laurent

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  • Surveys both analytical and numerical aspects of 1D hyperbolic balance laws
  • Presents a strategy for proving the accuracy of well-balanced numerical schemes
  • Compares several practical schemes, including wavefront tracking and 2D Riemann problems
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eBook 41,64 €
price for Spain (gross)
  • ISBN 978-3-319-24785-4
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover 51,99 €
price for Spain (gross)
  • ISBN 978-3-319-24784-7
  • 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
About this book

This monograph presents, in an attractive and self-contained form, techniques based on the L1 stability theory derived at the end of the 1990s by A. Bressan, T.-P. Liu and T. Yang that yield original error estimates for so-called well-balanced numerical schemes solving 1D hyperbolic systems of balance laws. Rigorous error estimates are presented for both scalar balance laws and a position-dependent relaxation system, in inertial approximation. Such estimates shed light on why those algorithms based on source terms handled like "local scatterers" can outperform other, more standard, numerical schemes. Two-dimensional Riemann problems for the linear wave equation are also solved, with discussion of the issues raised relating to the treatment of 2D balance laws. All of the material provided in this book is highly relevant for the understanding of well-balanced schemes and will contribute to future improvements.

Reviews

“The main purpose of the book is to present an analysis of global (in space) error bounds for well-balanced schemes with a specific emphasis on the time dependence of such bounds. … The book will be of interest to anyone willing to design and/or study well-balanced schemes, either from an analytical or practical point of view. … this book will surely contribute to future improvements in the field.” (Jean-François Coulombel, Mathematical Reviews, August, 2016)

“All of the material provided in this book is highly relevant for the understanding of well-balanced schemes and will contribute to future improvements. Each chapter is more or less self-containing, it has its own abstract, introduction and the list of references.” (Vit Dolejsi, zbMATH 1332.65132, 2016)


Table of contents (6 chapters)

Table of contents (6 chapters)

Buy this book

eBook 41,64 €
price for Spain (gross)
  • ISBN 978-3-319-24785-4
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover 51,99 €
price for Spain (gross)
  • ISBN 978-3-319-24784-7
  • 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
Error Estimates for Well-Balanced Schemes on Simple Balance Laws
Book Subtitle
One-Dimensional Position-Dependent Models
Authors
Series Title
SpringerBriefs in Mathematics
Copyright
2015
Publisher
Springer International Publishing
Copyright Holder
The Author(s)
eBook ISBN
978-3-319-24785-4
DOI
10.1007/978-3-319-24785-4
Softcover ISBN
978-3-319-24784-7
Series ISSN
2191-8198
Edition Number
1
Number of Pages
XV, 110
Number of Illustrations
9 b/w illustrations, 15 illustrations in colour
Topics