Numerical Methods for Conservation Laws

Randall J. Leveque

ISBN 10: 3764327235 / ISBN 13: 9783764327231

Published by Birkhäuser Basel, 1992

About this Item

Druck auf Anfrage Neuware - Printed after ordering - These notes were developed for a graduate-level course on the theory and numerical solution of nonlinear hyperbolic systems of conservation laws. Part I deals with the basic mathematical theory of the equations: the notion of weak solutions, entropy conditions, and a detailed description of the wave structure of solutions to the Riemann problem. The emphasis is on tools and techniques that are indispensable in developing good numerical methods for discontinuous solutions. Part II is devoted to the development of high resolution shock-capturing methods, including the theory of total variation diminishing (TVD) methods and the use of limiter functions. The book is intended for a wide audience, and will be of use both to numerical analysts and to computational researchers in a variety of applications.

Seller Inventory # 9783764327231

Bibliographic Details

• Title: Numerical Methods for Conservation Laws
• Publisher: Birkhäuser Basel
• Publication Date: 1992
• Language: English
• ISBN 10: 3764327235
• ISBN 13: 9783764327231
• Binding: Taschenbuch
• Edition: 2nd Edition
• Condition: Neu
• Dimensions: 244W x 170H x 13D millimeters 244 millimeters width by 170 millimeters height by 13 millimeters depth
• Weight: 409 grams

About this title

Synopsis

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 de­ veloping, analyzing, and successfully using numerical methods for nonlinear systems of conservation laws, particularly for problems involving shock waves. A reasonable un­ derstanding 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 present­ ing 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. Without 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.

Review

"The computing community needs a good text on modern methods for conservation laws, and these notes provide an excellent start on that text. Equally important, LeVeque's perspective and writing style make for wonderful reading and learning. (How often do we find important content and good writing in one book?)"   ―SIAM Review

"The book by Randall LeVeque is among the first that makes the material in this area accessible to first and second year graduate students in the mathematical sciences. It should be an excellent introduction to this topic for any researcher in the mathematical sciences...This book is based on [the] lecture notes of the author and should serve well as a text for a graduate course...There are many interesting exercises that serve to illuminate and expand on the text, and there are also many well-drawn figures."   ―Bulletin of the AMS