Elliptic Differential Equations Theory and Numerical Treatment
This book simultaneously presents the theory and the numerical treatment of elliptic boundary value problems, since an understanding of the theory is necessary for the numerical analysis of the discretisation. It first discusses the Laplace equation and i
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Wolfgang Hackbusch
Elliptic Differential Equations Theory and Numerical Treatment Second Edition
Springer Series in Computational Mathematics 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
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Wolfgang Hackbusch
Elliptic Differential Equations Theory and Numerical Treatment Second Edition
Wolfgang Hackbusch MPI für Mathematik in den Naturwissenschaften Leipzig, Germany
Original first edition W. Hackbusch, Theorie und Numerik elliptischer Differentialgleichungen, B.G. Teubner, Stuttgart 1987.
ISSN 0179-3632 ISSN 2198-3712 (electronic) Springer Series in Computational Mathematics ISBN 978-3-662-54960-5 ISBN 978-3-662-54961-2 (eBook) DOI 10.1007/978-3-662-54961-2 Library of Congress Control Number: 2017942725 Mathematics Subject Classification (2010): 35J05, 35J08, 35J15, 35J20, 35J25, 35J30, 35J40, 35J50, 65N06, 65N12, 65N15, 65N22, 65N25, 65N30, 65N50, 65N80, 65M50, 35S15 © Springer-Verlag GmbH Germany 1992, 2017 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. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer-Verlag GmbH Germany The registered company address is: Heidelberger Platz 3, 14197 Berlin, Germany
For my granddaughter Finja
Preface
This book has developed from lectures that the author gave for mathematics students at the Ruhr-Universit¨at Bochum and the Christian-Albrechts-Universit¨at Kiel. The present work is restricted to the theory of partial differential equations of elliptic type, which otherwise tends to be given a treatment which is either too superficial or too extensive. The following sketch shows what the problems are for elliptic differential equations. A: B: Discretisation: Theory of difference methods, elliptic finite elements, etc. equations ↑ ↓ Ell
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