Numerical Methods for Conservation Laws
These notes developed from a course on the numerical solution of conservation laws first taught at the University of Washington in the fall of 1988 and then at ETH during the following spring. The overall emphasis is on studying the mathematical tools tha
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Numerical Methods for Conservation Laws
Randall J . LeVeque Numerical Methods for Conservation Laws
1990
Springer Basel AG
Author's address: Randall J. LeVeque Department of Mathematics, GN-50 University of Washington Seattle, WA 98195 USA
Deutsche Bibliothek Cataloguing-in-Publication Data
LeVeque, Randall J.: Numerical methods for conservation laws / Randall J. LeVeque. - Basel; Boston; Berlin: Birkhäuser 1990 (Lectures in mathematics) ISBN 978-3-7643-2464-3 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. Under § 54 of the German Copyright Law where copies are made for other than private use a fee is payable to «Verwertungsgesellschaft Wort», Munich.
© Springer Basel AG 1990 Originally published by Birkhäuser Verlag, Basel in 1990 Printed on acid-free paper ISBN 978-3-7643-2464-3 DOI 10.1007/978-3-0348-5116-9
ISBN 978-3-0348-5116-9 (eBook)
Preface These notes developed from a course on the numerical solution of conservation laws first taught at the University of Washington in the fall of 1988 and then at ETH during the following spring. The overall emphasis is on studying the mathematical tools that are essential in developing, analyzing, and successfully using numerical methods for nonlinear systems of conservation laws, particularly for problems involving shock waves. A reasonable understanding of the mathematical structure of these equations and their solutions is first required, and Part I of these notes deals with this theory. Part II deals more directly with numerical methods, again with the emphasis on general tools that are of broad use. I have stressed the underlying ideas used in various classes of methods rather than presenting the most sophisticated methods in great detail. My aim was to provide a sufficient background that students could then approach the current research literature with the necessary tools and understanding. vVithout the wonders of TeX and LaTeX, these notes would never have been put together. The professional-looking results perhaps obscure the fact that these are indeed lecture notes. Some sections have been reworked several times by now, but others are still preliminary. I can only hope that the errors are not too blatant. Moreover, the breadth and depth of coverage was limited by the length of these courses, and some parts are rather sketchy. I do have hopes of eventually expanding these notes into a fullfledged book, going more deeply into some areas, discussing a wider variety of methods and techniques, and including discussions of more applications areas. For this reason I am particularly interested in receiving corrections, comments and suggestions. I can be reached via electronic mail at [email protected]. I am indebted to Jiirgen Moser and the Forschungsinstitut at ETH for the opportunity to visit and spend time dev
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