Correction to: The Hybrid High-Order Method for Polytopal Meshes
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Daniele Antonio Di Pietro Jérôme Droniou
The Hybrid HighOrder Method for Polytopal Meshes Design, Analysis, and Applications
MS&A Volume 19
Editor-in-Chief Alfio Quarteroni Series Editors Tom Hou Claude Le Bris Anthony T. Patera Enrique Zuazua
More information about this series at http://www.springer.com/series/8377
Daniele Antonio Di Pietro • Jérôme Droniou
The Hybrid High-Order Method for Polytopal Meshes Design, Analysis, and Applications
Daniele Antonio Di Pietro Institut Montpelliérain Alexander Grothendieck Université de Montpellier Montpellier, France
Jérôme Droniou School of Mathematics Monash University Clayton VIC, Australia
ISSN 2037-5255 ISSN 2037-5263 (electronic) MS&A ISBN 978-3-030-37202-6 ISBN 978-3-030-37203-3 (eBook) https://doi.org/10.1007/978-3-030-37203-3 © Springer Nature Switzerland AG 2020 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, expressed 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. Cover illustration by the Authors: Streamlines for the three-dimensional lid-driven cavity flow on a Voronoi mesh This Springer imprint is published by the registered company Springer Nature Switzerland AG. The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
Preface
Originally introduced in [146, 158], Hybrid High-Order (HHO) methods provide a framework for the discretisation of models based on Partial Differential Equations (PDEs) with features that set them apart from traditional ones. The construction hinges on discrete unknowns that are broken polynomials on the mesh and on its skeleton, from which two key ingredients are devised: 1. Local reconstructions obtained by solving small, embarrassingly parallel problems inside each element, and typically conceived so that their composition with the natural interpolator of sufficiently smooth functions yields a physics- and problem-dependent projector on local polynomial spaces; 2. Stabilisation terms that penalise
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