A Numerical Study of Averaging Error Indicators in p-FEM

We consider the averaging error indicator in the context of the p-FEM. We explain how a proof of reliability and efficiency might look, and why the error indicator will behave differently than for low order methods. Using two model problems, one with nons

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Mejdi Azaïez · Henda El Fekih Jan S. Hesthaven Editors

Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2012 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

For further volumes: http://www.springer.com/series/3527

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Mejdi Azaïez  Henda El Fekih Jan S. Hesthaven Editors

Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2012 Selected papers from the ICOSAHOM conference, June 25-29, 2012, Gammarth, Tunisia

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Editors Mejdi Azaïez Institut Polytechnique de Bordeaux Université de Bordeaux Pessac, France

Henda El Fekih Ecole Nationale d’Ingénieurs de Tunis Université de Tunis El Manar Tunis, Tunisia

Jan S. Hesthaven Ecole Polytechnique Fédérale de Lausanne EPFL-SB-MATHICSE-MCSS Lausanne, Switzerland

ISSN 1439-7358 ISBN 978-3-319-01600-9 ISBN 978-3-319-01601-6 (eBook) DOI 10.1007/978-3-319-01601-6 Springer Cham Heidelberg New York Dordrecht London Mathematics Subject Classification (2010): Primary: 65M70; 65N35; 65N30; 74S25; 76M10; 76M22; 78M10; 78M22 Secondary: 33Cxx; 41Axx; 65Cxx; 65Dxx; 65Lxx; 65Mxx; 65Nxx; 74Jxx; 76Mxx; 78Mxx; 80Mxx76 c 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 mate