Least-Squares Finite Element Methods
The book examines theoretical and computational aspects of least-squares finite element methods(LSFEMs) for partial differential equations (PDEs) arising in key science and engineering applications. It is intended for mathematicians, scientists, and engin
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Least-Squares Finite Element Methods 13
Applied Mathematical Sciences Volume 166 Editors S.S. Antman J.E. Marsden L. Sirovich
Advisors J.K. Hale P. Holmes J. Keener J. Keller B.J. Matkowsky A. Mielke C.S. Peskin K.R. Sreenivasan
For further volumes: http://www.springer.com/series/34
Pavel B. Bochev
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Max D. Gunzburger
Least-Squares Finite Element Methods
123
Pavel B. Bochev Sandia National Laboratories Applied Mathematics and Applications MS 1320, P.O. Box 5800 Albuquerque NM 87185-1320 USA [email protected]
Max D. Gunzburger Florida State University Department of Scientific Computing 400 Dirac Science Library Tallahassee FL 32306-4120 USA [email protected]
Editors: S.S. Antman Department of Mathematics and Institute for Physical Science and Technology University of Maryland College Park MD 20742-4015 USA [email protected]
J.E. Marsden Control and Dynamical Systems, 107-81 California Institute of Technology Pasadena, CA 91125 USA [email protected]
ISBN 978-0-387-30888-3 DOI 10.1007/978-0-387-68922-7
L. Sirovich Laboratory of Applied Mathematics Department of Biomathematical Sciences Mount Sinai School of Medicine New York, NY 10029-6574 USA [email protected]
e-ISBN 978-0-387-68922-7
Library of Congress Control Number: 2008943966 Mathematics Subject Classification (2000): 65N30, 65N35, 65N12, 65N21, 65M60, 65M70, 65M12 c Springer Science+Business Media, LLC 2009 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed on acid-free paper springer.com
To my mother and Biliana To Janet
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Preface
Since their emergence in the early 1950s, finite element methods have become one of the most versatile and powerful methodologies for the approximate numerical solution of partial differential equations. At the time of their inception, finite element methods were viewed primarily as a tool for solving problems in structural analysis. However, it did not take long to discover that finite element methods could be applied with equal success to problems in other engineering and scientific fields. Today, finite element methods are also in common use, and indeed are often the method of choice, for incompressible fluid flow, heat transfer, electromagnetics, and advection-diffusion-reaction problems, just to name a few. Given the early connection between finite element methods and problems engendered by energy minimization principles, it i
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