IsoGeometric Analysis: A New Paradigm in the Numerical Approximation of PDEs
Providing an introduction to isogeometric methods with a focus on their mathematical foundations, this book is composed of four chapters, each devoted to a topic of special interests for isogeometric methods and their theoretical understanding. It contain
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Annalisa Buffa Giancarlo Sangalli Editors
IsoGeometric Analysis: A New Paradigm in the Numerical Approximation of PDEs Cetraro, Italy 2012
Lecture Notes in Mathematics Editors-in-Chief: J.-M. Morel, Cachan B. Teissier, Paris Advisory Board: Camillo De Lellis, Zurich Mario di Bernardo, Bristol Alessio Figalli, Zurich Davar Khoshnevisan, Salt Lake City Ioannis Kontoyiannis, Athens Gabor Lugosi, Barcelona Mark Podolskij, Aarhus Sylvia Serfaty, Paris and New York Catharina Stroppel, Bonn Anna Wienhard, Heidelberg
More information about this series at http://www.springer.com/series/304
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Annalisa Buffa • Giancarlo Sangalli Editors
IsoGeometric Analysis: A New Paradigm in the Numerical Approximation of PDEs Cetraro, Italy 2012
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Editors Annalisa Buffa IMATI - CNR Pavia, Italy
ISSN 0075-8434 Lecture Notes in Mathematics ISBN 978-3-319-42308-1 DOI 10.1007/978-3-319-42309-8
Giancarlo Sangalli Dipartimento di Matematica Università di Pavia Pavia, Italy
ISSN 1617-9692 (electronic) ISBN 978-3-319-42309-8 (eBook)
Library of Congress Control Number: 2016954372 Mathematics Subject Classification (2010): 65N30 © Springer International Publishing Switzerland 2016 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. Cover illustration: deblik, Berlin Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer International Publishing AG Switzerland
Preface
Isogeometric analysis (IGA) refers to a collection of methods, first introduced by T.J.R. Hughes and collaborators in the seminal paper [3], that use splines, or some of their generalisations such as NURBS (non-uniform rational B-splines), T-splines and hierarchical splines, as functions to build approximation spaces which are then used to numerically solve partial differential equations (PDEs). Indeed, splines and their extensions are the basic mathematical engine behind CAD systems, and one of the main motivation for IGA was to design numerical methods able to avoid
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