Boundary Element Methods
This work presents a thorough treatment of boundary element methods (BEM) for solving strongly elliptic boundary integral equations obtained from boundary reduction of elliptic boundary value problems in IR3. The book is self-contained, the prerequi
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Stefan A. Sauter
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Christoph Schwab
B oundary Element M ethods
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Stefan A. Sauter Universität Zürich Institut für Mathematik Winterthurerstr. 190 8057 Zürich Switzerland [email protected]
Christoph Schwab ETH Zürich Seminar für Angewandte Mathematik Rämistrasse 101 8092 Zürich Switzerland [email protected]
Translation and expanded edition from the German language edition: Randelementmethoden, © Teubner 2004. Vieweg+Teubner is part of Springer Science and Business Media, All Rights Reserved
ISSN 0179-3632 ISBN 978-3-540-68092-5 e-ISBN 978-3-540-68093-2 DOI 10.1007/978-3-540-68093-2 Springer Heidelberg Dordrecht London New York
Mathematics Subject Classification (2010): 45B05, 65F10, 65N38, 65R20, 65D32, 65F50, 78M16 c Springer-Verlag Berlin Heidelberg 2011 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, 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. Cover design: deblik, Berlin Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
We dedicate this book to Annika, Lina, and Gaby
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Preface
The integral equation method is an elegant mathematical way of transforming elliptic partial differential equations (PDEs) into boundary integral equations (BIEs). The focus of this book is the systematic development of efficient numerical methods for the solution of these boundary integral equations and therefore of the underlying differential equations. The integral equation method has a long history that is closely linked to mathematicians such as I. Fredholm, D. Hilbert, E. Nystr¨om, J. Hadamard, J. Plemelj, J. Radon and many others. Here is a list of some of the original works on the subject: [46, 96, 101, 126, 164, 165, 173, 175–177, 181, 182, 188, 214, 229]. With the introduction of variational methods for partial differential equations at the beginning of the twentieth century, integral equations lost some of their importance for the area of analysis. This was due to the difficulty of formulating precise results on existence and uniqueness by means of classical integral equations. Since the middle of the twentieth century the need for numerical methods for partial differential methods began to grow. This was reflected also in the rapidly incre
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