BEM-based Finite Element Approaches on Polytopal Meshes
This book introduces readers to one of the first methods developed for the numerical treatment of boundary value problems on polygonal and polyhedral meshes, which it subsequently analyzes and applies in various scenarios. The BEM-based finite element app
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Steffen Weißer
BEM-based Finite Element Approaches on Polytopal Meshes Editorial Board T. J.Barth M.Griebel D.E.Keyes R.M.Nieminen D.Roose T.Schlick
Lecture Notes in Computational Science and Engineering Editors: Timothy J. Barth Michael Griebel David E. Keyes Risto M. Nieminen Dirk Roose Tamar Schlick
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More information about this series at http://www.springer.com/series/3527
Steffen Weißer
BEM-based Finite Element Approaches on Polytopal Meshes
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Steffen Weißer FR Mathematik Universit¨at des Saarlandes Saarbr¨ucken, Germany
ISSN 1439-7358 ISSN 2197-7100 (electronic) Lecture Notes in Computational Science and Engineering ISBN 978-3-030-20960-5 ISBN 978-3-030-20961-2 (eBook) https://doi.org/10.1007/978-3-030-20961-2 Mathematics Subject Classification (2010): 65N15, 65N30, 65N38, 65N50, 65D05, 41A25, 41A30 © Springer Nature Switzerland AG 2019 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. This Springer imprint is published by the registered company Springer Nature Switzerland AG. The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
To Anna
Preface
The BEM-based finite element method has been developed within the last decade, and it is one of the first methods designed for the approximation of boundary value problems on polygonal and polyhedral meshes. This is possible due to the use of implicitly defined ansatz functions which are treated locally by means of boundary integral operators and are realized with the help of boundary element methods (BEM) in the computations. When I started my doctoral studies in 2009, it was an appealing but also a somehow abstruse idea to generalize the well-known finite element method (FEM) to polygonal and polyhedral meshes. To that time, I was not aware of any other attempts in this direction. A few years later, the virtual element method came up, and I learned about other approac
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