Overview
- 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
- Includes supplementary material: sn.pub/extras
Part of the book series: SpringerBriefs in Mathematics (BRIEFSMATH)
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Table of contents (6 chapters)
Keywords
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)
Authors and Affiliations
Bibliographic Information
Book Title: Error Estimates for Well-Balanced Schemes on Simple Balance Laws
Book Subtitle: One-Dimensional Position-Dependent Models
Authors: Debora Amadori, Laurent Gosse
Series Title: SpringerBriefs in Mathematics
DOI: https://doi.org/10.1007/978-3-319-24785-4
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Author(s) 2015
Softcover ISBN: 978-3-319-24784-7Published: 23 November 2015
eBook ISBN: 978-3-319-24785-4Published: 23 October 2015
Series ISSN: 2191-8198
Series E-ISSN: 2191-8201
Edition Number: 1
Number of Pages: XV, 110
Number of Illustrations: 9 b/w illustrations, 15 illustrations in colour
Topics: Partial Differential Equations, Numerical Analysis, Mathematical Applications in the Physical Sciences, Numerical and Computational Physics, Simulation