A Moving Least Squares Approach to the Construction of Discontinuous Enrichment Functions
In this paper we are concerned with the construction of a piecewise smooth field from scattered data by a moving least squares approach. This approximation problem arises when so-called enrichment functions for a generalized finite element method are comp
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Singular Phenomena and Scaling in Mathematical Models
Singular Phenomena and Scaling in Mathematical Models
Michael Griebel Editor
Singular Phenomena and Scaling in Mathematical Models
123
Editor Michael Griebel Institut f¨ur Numerische Simulation Universit¨at Bonn Bonn Germany
ISBN 978-3-319-00785-4 ISBN 978-3-319-00786-1 (eBook) DOI 10.1007/978-3-319-00786-1 Springer Cham Heidelberg New York Dordrecht London Library of Congress Control Number: 2013948877 Math. Subj. Class. (2010): 00B15, 00A69, 00A71, 00A99, 26A30, 35A20, 35B65, 60J60, 65N12, 65Z05 © Springer International Publishing Switzerland 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
The success of quantitative modeling in the rapidly expanding areas of the natural sciences, such as materials science and biology, produces a variety of new mathematical models. The predictive power of these models has to be tested, and methods for their effective treatment have to be developed. This major opportunity for mathematics led to the foundation of the Collaborative Research Center SFB 611 entitled ‘Singular Phenomena and Scaling in Mathematical Models’ at the University of Bonn in 2002. One of its major goals was the efficient handling of new types of models through the close combination o
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