Hyperbolic Partial Differential Equations Theory, Numerics and Appli
The book gives an introduction to the fundamental properties of hyperbolic partial differential equations und their appearance in the mathematical modeling of various problems from practice. It shows in an unique manner concepts for the numerical treatmen
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Hyperbolic Partial Differential Equations
Andreas Meister Jens Struckmeier
Hyperbolic Partial Differential Equations Theory, Numerics and Applications
II vleweg
Hochschuldozent Dr. Andreas Meister Medizinische Universitat zu Lubeck Institut fur Mathematik WallstraBe 40 D-23560 Lubeck, Germany Professor Dr. Jens Struckmeier Universitat Hamburg Fachbereich Mathematik BundesstraBe 55 D-20146 Hamburg, Germany [email protected] [email protected]
Die Deutsche Bibliothek - CIP-Cataloguing-in-Publication-Data A catalogue record for this publication is available from Die Deutsche Bibliothek.
First edition, March 2002
All rights reserved © Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig/Wiesbaden, 2002 Softcove r re print of the hardcover 1st edition 2002 Vieweg is a company in the specialist publishing group BertelsmannSpringer. www.vieweg.de
No part of this publication may be reproduced, stored in a retrieval system or transmitted, mechanical, photocopying or otherwise without prior permission of the copyright holder.
Cover design: Ulrike Weigel, www.CorporateDesignGroup.de Printed on acid-free paper
ISBN -13 : 978-3-322-80229·3 e-ISBN -13: 978-3-322-80227·9 DOl: 10.1007/978-3-322-80227·9
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Preface The following chapters summarize lectures given in March 2001 during the summerschool on Hyperbolic Partial Differential Equations which took place at the Technical University of Hamburg-Harburg in Germany. This type of meeting is originally funded by the Volkswagenstiftung in Hannover (Germany) with the aim to bring together well-known leading experts from special mathematical, physical and engineering fields of interest with PhDstudents, members of Scientific Research Institutes as well as people from Industry, in order to learn and discuss modern theoretical and numerical developments. Hyperbolic partial differential equations play an important role in various applications from natural sciences and engineering. Starting from the classical Euler equations in fluid dynamics, several other hyperbolic equations arise in traffic flow problems, acoustics, radiation transfer, crystal growth etc. The main interest is concerned with nonlinear hyperbolic problems and the special structures, which are characteristic for solutions of these equations, like shock and rarefaction waves as well as entropy solutions. As a consequence, even numerical schemes for hyperbolic equations differ significantly from methods for elliptic and parabolic equations: the transport of information runs along the characteristic curves of a hyperbolic equation and consequently the direction of transport is of constitutive importance. This property leads to the construction of upwind schemes and the theory of Riemann solvers. Both concepts are combined with explicit or implicit time stepping techniques whereby the chosen order of accuracy usually depends on the expected dynamic of the underlying solution. Numerical schemes for hyperbolic equations should always satisfy two contrary goals: • smooth solutions shoul
