Analysis of Finite Difference Schemes For Linear Partial Differentia
This book develops a systematic and rigorous mathematical theory of finite difference methods for linear elliptic, parabolic and hyperbolic partial differential equations with nonsmooth solutions.
Finite difference methods are a classical class of techni
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Boško S. Jovanovi´c r Endre Süli
Analysis of Finite Difference Schemes For Linear Partial Differential Equations with Generalized Solutions
Boško S. Jovanovi´c Faculty of Mathematics University of Belgrade Belgrade, Serbia
Endre Süli Mathematical Institute University of Oxford Oxford, UK
ISSN 0179-3632 Springer Series in Computational Mathematics ISBN 978-1-4471-5459-4 ISBN 978-1-4471-5460-0 (eBook) DOI 10.1007/978-1-4471-5460-0 Springer London Heidelberg New York Dordrecht Library of Congress Control Number: 2013952460 Mathematics Subject Classification: 65M06, 65M08, 65M12, 65M15, 65N06, 65N08, 65N12, 65N15 © Springer-Verlag London 2014 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. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the Copyright Clearance Center. Violations are liable to prosecution under the respective Copyright Law. 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. While the advice and information in this book are believed to be true and accurate at the date of publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
Preface
Boundary-value problems and initial-boundary-value problems for partial differential equations of continuum mechanics and mathematical physics that arise in applications in the physical sciences and engineering frequently contain ‘nonsmooth’ or ‘singular’ data, such as jumps in the coefficients in the equation, caused by discontinuities in material properties, or concentrated loads that are modelled as point sources, or indeed discontinuities in the solution at interfaces in transmission problems. There is a wealth
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