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Error Estimates for Well-Balanced Schemes on Simple Balance Laws

One-Dimensional Position-Dependent Models

  • Debora Amadori
  • Laurent Gosse
Book

Part of the SpringerBriefs in Mathematics book series (BRIEFSMATH)

Table of contents

  1. Front Matter
    Pages i-xv
  2. Debora Amadori, Laurent Gosse
    Pages 1-7
  3. Debora Amadori, Laurent Gosse
    Pages 9-22
  4. Debora Amadori, Laurent Gosse
    Pages 23-44
  5. Debora Amadori, Laurent Gosse
    Pages 45-79
  6. Debora Amadori, Laurent Gosse
    Pages 81-90
  7. Debora Amadori, Laurent Gosse
    Pages 91-107
  8. Back Matter
    Pages 109-110

About this book

Introduction

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.

Keywords

Hyperbolic systems of balance laws Glimm-Liu-Bressan L1 stability theory Error estimates for well-balanced schemes Local scattering centers Two-dimensional Riemann problem

Authors and affiliations

  • Debora Amadori
    • 1
  • Laurent Gosse
    • 2
  1. 1.DISIMUniversità degli Studi dell'AquilaL'AquilaItaly
  2. 2.Istituto per le Applicazioni del Calcolo "Mauro Picone"CNRRomaItaly

Bibliographic information