Galerkin Finite Element Methods for Parabolic Problems
My purpose in this monograph is to present an essentially self-contained account of the mathematical theory of Galerkin finite element methods as applied to parabolic partial differential equations. The emphases and selection of topics reflects my own inv
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Springer-Verlag Berlin Heidelberg GmbH
Vidar Thomee
Galerkin Finite Element Methods for Parabolic Problems
Springer
Vidar Thomee Department of Mathematics Chalmers University of Technology S-41296 Goteborg Sweden e-mail: [email protected]
Cataloging-in-Publication Data applied for
Die Deutsche Bibliothek - CIP-Einheitsaufnahme Thomee, Vidar: Galerkin finite element methods for parabolic problems / Vidar Thomee. - Berlin ; Heidelberg; New York ; Barcelona ; Budapest ; Hong Kong; London; Milan; Paris; Santa Qara ; Singapore; Tokyo : Springer, 1997 (Springer series in computational mathematics ; 25)
Mathematics Subject Classification (1991): 65M60, 65M12, 65M15
ISSN 0179-3632 ISBN 978-3-662-03361-6 ISBN 978-3-662-03359-3 (eBook) DOI 10.1007/978-3-662-03359-3 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from SpringerVerlag. Violations are liable for prosecution under the German Copyright Law. © Springer-Verlag Berlin Heidelberg 1997 Originally published by Springer-Verlag Berlin Heidelberg New York in 1997. Softcover reprint of the hardcover I st edition 1997 The use of general descriptive names, registered names, trademarks, 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. Typesetting: Camera-ready copy produced from the author's output file using a Springer TEX macro package 41/3143 - 5 4321 0 - Printed on acid-free paper SPIN 10521927
Preface
My purpose in this monograph is to present an essentially self-contained account of the mathematical theory of Galerkin finite element methods as applied to parabolic partial differential equations. The emphases and selection of topics reflects my own involvement in the field over the past 25 years, and my ambition has been to stress ideas and methods of analysis rather than to describe the most general and farreaching results possible. Since the formulation and analysis of Galerkin finite element methods for parabolic problems are generally based on ideas and results from the corresponding theory for stationary elliptic problems, such material is often included in the presentation. The basis of this work is my earlier text entitled Galerkin Finite Element Methods for Parabolic Problems, Springer Lecture Notes in Mathematics, No. 1054, from 1984. This has been out of print for several years, and I have felt a need and been encouraged by colleagues and friends to publish an updated version. In doing so I have included most of the contents of the 14 chapters of
