Mixed and Hybrid Finite Element Methods
Research on non-standard finite element methods is evolving rapidly and in this text Brezzi and Fortin give a general framework in which the development is taking place. The presentation is built around a few classic examples: Dirichlet's problem, Stokes
- PDF / 26,044,132 Bytes
- 361 Pages / 439.364 x 666.137 pts Page_size
- 37 Downloads / 405 Views
15
Editorial Board R.L. Graham, Murray Hill (NJ) J. Stoer, WOrzburg R. Varga, Kent (Ohio)
Franco Brezzi
Michel Fortin
Mixed and Hybrid Finite Element Methods With 65 Illustrations
Springer-Verlag New York Berlin Heidelberg London Paris Tokyo Hong Kong Barcelona
Franco Brezzi University of Pavia Institute of Numerical Analysis 5 Corso Carlo Alberto 1-271 00 Pavia Italy
Michel Fortin Departement de MatMmatiques et de Statistique Universite Laval Quebec G1 K 7P4 Canada
Mathematics Subject Classification: 73XX, 76XX
library of Congress Cataloging-in-Publication Data Breul, Franco. Mixed alld hybrid finite element methods ' Franco Breul, Michel Fortin. p. cm -- (Springer series in computational mathematics: t5) Includes bibliographical references and index.
ISBN-13: 978-1-46]2-7824-5 ~-ISBN-13: 978-1-4612-3172-1 001: IO.l007f978-]-4612-3172-] 1. Finite element method. I. Breai, F. (Franco),1945-. II. TItle. III. Series. TA347.F5F68 1991 620'.00t'51535--dc20 9t-t0909 Printed on acid-free paper.
© 1991 Springer-Verlag New YorK Inc.
Softcover reprint of the hardcover 1st edition 1991 All rights reserved. This work may not be translated or copied in whole or in part without the written permission 01 the publisher (Springer-Verlag New YorK, Inc., 175 Filth Avenue, New YorK, NY 10010, USA), except for briel excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information and retrieval, electronic adaptation, computer software, or by similaror dissimilar methodology now known or hereafter developed is forbidden. The use of general descriptive names, trade names, trademarKs, etc., in this publication, even if the former are not especiafly identified, is not to be taken as a sign thal such names, as understood by the Trade Marks and Merchandise Marks Act, may accordingly be used freely by anyone. Photocomposed COpy prepared from the author's TEX file.
9 8 7 6 5
321 4
Preface
When, a few years ago, we began the redaction of this book, we had the naive thought that the theory of mixed and hybrid finite element methods was ripe enough for a unified presentation. We soon realized that things were not so simple and that, if basic facts were known, many obscure zones remained in many applications. Indeed the literature about nonstandard finite element method is still evolving rapidly and this book cannot pretend to be complete. We would rather like to lead the reader through the general framework in which development is taking place. We have therefore built our presentation around a few classical examples: Dirichlet's problem, Stokes problem, linear elasticity, ... They are sketched in Chapter I and basic methods to approximate them are presented in Chapter IV, following the general theory of Chapter II and using finite element spaces of Chapter III. Those four chapters are therefore the essential part of the book. They are complemented by the following three chapters which present a more detailed analysis of some problems. Chapter V comes back to mixed approximations of Diri
