Discontinuous Galerkin Method Analysis and Applications to Compressi
The subject of the book is the mathematical theory of the discontinuous Galerkin method (DGM), which is a relatively new technique for the numerical solution of partial differential equations. The book is concerned with the DGM developed for elliptic and
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Vít Dolejší Miloslav Feistauer
Discontinuous Galerkin Method Analysis and Applications to Compressible Flow
Springer Series in Computational Mathematics Volume 48
Editorial Board R.E. Bank R.L. Graham W. Hackbusch J. Stoer R.S. Varga H. Yserentant
More information about this series at http://www.springer.com/series/797
Vít Dolejší Miloslav Feistauer •
Discontinuous Galerkin Method Analysis and Applications to Compressible Flow
123
Vít Dolejší Faculty of Mathematics and Physics Charles University in Prague Praha 8 Czech Republic
Miloslav Feistauer Faculty of Mathematics and Physics Charles University in Prague Praha 8 Czech Republic
ISSN 0179-3632 ISSN 2198-3712 (electronic) Springer Series in Computational Mathematics ISBN 978-3-319-19266-6 ISBN 978-3-319-19267-3 (eBook) DOI 10.1007/978-3-319-19267-3 Library of Congress Control Number: 2015943371 Mathematics Subject Classification (2010): 65M60, 65M15, 65M20, 65M08, 65N30, 65N15, 76M10, 76M12, 35D30 Springer Cham Heidelberg New York Dordrecht London © Springer International Publishing Switzerland 2015 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper Springer International Publishing AG Switzerland is part of Springer Science+Business Media (www.springer.com)
Preface
Many real-world problems are described by partial differential equations whose numerical solution represents an important part of numerical mathematics. There are several techniques for their solution: the finite difference method, the finite element method, spectral methods and the finite volume method. All these methods have advantages as well as disadvantages. The first three techniques are suitable particularly for problems in which the exact solution is sufficiently regular. The presence of interior and boundary layers appearing in solutions of singularly perturbed problems (e.g., convection-diffusion problems with dominating convection) or discontinuities in solutions of nonlinear hyperbolic equations lead to some difficulti
