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Numerical Approximation of Hyperbolic Systems of Conservation Laws

  • Edwige Godlewski
  • Pierre-Arnaud Raviart

Part of the Applied Mathematical Sciences book series (AMS, volume 118)

Table of contents

  1. Front Matter
    Pages i-viii
  2. Edwige Godlewski, Pierre-Arnaud Raviart
    Pages 1-36
  3. Edwige Godlewski, Pierre-Arnaud Raviart
    Pages 37-98
  4. Edwige Godlewski, Pierre-Arnaud Raviart
    Pages 99-166
  5. Edwige Godlewski, Pierre-Arnaud Raviart
    Pages 167-302
  6. Edwige Godlewski, Pierre-Arnaud Raviart
    Pages 303-416
  7. Edwige Godlewski, Pierre-Arnaud Raviart
    Pages 417-460
  8. Back Matter
    Pages 461-510

About this book

Introduction

This work is devoted to the theory and approximation of nonlinear hyper­ bolic systems of conservation laws in one or two space variables. It follows directly a previous publication on hyperbolic systems of conservation laws by the same authors, and we shall make frequent references to Godlewski and Raviart (1991) (hereafter noted G. R. ), though the present volume can be read independently. This earlier publication, apart from a first chap­ ter, especially covered the scalar case. Thus, we shall detail here neither the mathematical theory of multidimensional scalar conservation laws nor their approximation in the one-dimensional case by finite-difference con­ servative schemes, both of which were treated in G. R. , but we shall mostly consider systems. The theory for systems is in fact much more difficult and not at all completed. This explains why we shall mainly concentrate on some theoretical aspects that are needed in the applications, such as the solution of the Riemann problem, with occasional insights into more sophisticated problems. The present book is divided into six chapters, including an introductory chapter. For the reader's convenience, we shall resume in this Introduction the notions that are necessary for a self-sufficient understanding of this book -the main definitions of hyperbolicity, weak solutions, and entropy­ present the practical examples that will be thoroughly developed in the following chapters, and recall the main results concerning the scalar case.

Keywords

Approximation Finite Mathematica Scala Scheme conservation law dynamics hyperbolic system online solution variable

Authors and affiliations

  • Edwige Godlewski
    • 1
  • Pierre-Arnaud Raviart
    • 2
  1. 1.Laboratoire d’Analyse NumériqueUniversité Pierre et Marie CurieParis Cedex 05France
  2. 2.Centre de Mathématiques AppliquéesEcole PolytechniquePalaiseau CedexFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-0713-9
  • Copyright Information Springer-Verlag New York 1996
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-6878-9
  • Online ISBN 978-1-4612-0713-9
  • Series Print ISSN 0066-5452
  • Series Online ISSN 2196-968X
  • Buy this book on publisher's site