The Mathematical Theory of Finite Element Methods.pdf-资料库

qq_38379932-10817351-4744302542860418943.pdf-第1页.png

第1页 / 共404页

qq_38379932-10817351-4744302542860418943.pdf-第2页.png

第2页 / 共404页

qq_38379932-10817351-4744302542860418943.pdf-第3页.png

第3页 / 共404页

qq_38379932-10817351-4744302542860418943.pdf-第4页.png

第4页 / 共404页

qq_38379932-10817351-4744302542860418943.pdf-第5页.png

第5页 / 共404页

qq_38379932-10817351-4744302542860418943.pdf-第6页.png

第6页 / 共404页

qq_38379932-10817351-4744302542860418943.pdf-第7页.png

第7页 / 共404页

qq_38379932-10817351-4744302542860418943.pdf-第8页.png

第8页 / 共404页

Texts in Applied Mathematics 15 Editors J.E. Marsden L. Sirovich S.S. Antman Advisors G. Iooss P. Holmes D. Barkley M. Dellnitz P. Newton

Texts in Applied Mathematics 1. 2. 3. 4. 5. 6. Sirovich: Introduction to Applied Mathematics. Wiggins: Introduction to Applied Nonlinear Dynamical Systems and Chaos. Hale/Koc¸ak: Dynamics and Bifurcations. Chorin/Marsden: A Mathematical Introduction to Fluid Mechanics, 3rd ed. Hubbard/West: Differential Equations: A Dynamical Systems Approach: Ordinary Differential Equations. Sontag: Mathematical Control Theory: Deterministic Finite Dimensional Systems, 2nd ed. Perko: Differential Equations and Dynamical Systems, 3rd ed. Seaborn: Hypergeometric Functions and Their Applications. Pipkin: A Course on Integral Equations. 7. 8. 9. 10. Hoppensteadt/Peskin: Modeling and Simulation in Medicine and the Life 11. 12. 13. 14. Sciences, 2nd ed. Braun: Differential Equations and Their Applications, 4th ed. Stoer/Bulirsch: Introduction to Numerical Analysis, 3rd ed. Renardy/Rogers: An Introduction to Partial Differential Equations. Banks: Growth and Diffusion Phenomena: Mathematical Frameworks and Applications. Brenner/Scott: The Mathematical Theory of Finite Element Methods, 3rd ed. Van de Velde: Concurrent Scientiﬁc Computing. 15. 16. 17. Marsden/Ratiu: Introduction to Mechanics and Symmetry, 2nd ed. 18. Hubbard/West: Differential Equations: A Dynamical Systems Approach: Higher-Dimensional Systems. Kaplan/Glass: Understanding Nonlinear Dynamics. 19. 20. Holmes: Introduction to Perturbation Methods. 21. 22. Curtain/Zwart: An Introduction to Inﬁnite-Dimensional Linear Systems Theory. Thomas: Numerical Partial Differential Equations: Finite Difference Methods. Taylor: Partial Differential Equations: Basic Theory. 23. 24. Merkin: Introduction to the Theory of Stability of Motion. 25. 26. Naber: Topology, Geometry, and Gauge Fields: Foundations. Polderman/Willems: Introduction to Mathematical Systems Theory: A Behavioral Approach. Reddy: Introductory Functional Analysis with Applications to Boundary Value Problems and Finite Elements. 27. 28. Gustafson/Wilcox: Analytical and Computational Methods of Advanced 29. Engineering Mathematics. Tveito/Winther: Introduction to Partial Differential Equations: A Computational Approach (continued after index)

Susanne C. Brenner L. Ridgway Scott The Mathematical Theory of Finite Element Methods Third Edition ABC

Susanne C. Brenner Department of Mathematics and Center for Computation and Technology Louisiana State University Baton Rouge, LA 70803 USA brenner@math.lsu.edu L. Ridgway Scott University of Chicago Chicago, IL 60637 USA ridg@uchicago.edu Series Editors J.E. Marsden Control and Dynamic Systems, 107-81 California Institute of Technology Pasadena, CA 91125 USA L. Sirovich Division of Applied Mathematics Brown University Providence, RI 02912 USA S.S. Antman Department of Mathematics and Institute for Physical Science and Technology University of Maryland College Park, MD 20742-4015 USA ssa@math.umd.edu ISBN 978-0-387-75933-3 DOI: 10.1007/978-0-387-75934-0 e-ISBN 978-0-387-75934-0 Library of Congress Control Number: 2007939977 Mathematics Subject Classiﬁcation (2000): 65N30, 65–01, 46N40, 65M60, 74S05 c 2008 Springer Science+Business Media, LLC 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 9 8 7 6 5 4 3 2 1 springer.com

Series Preface Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scientiﬁc disciplines and a resurgence of interest in the modern as well as the clas- sical techniques of applied mathematics. This renewal of interest, both in research and teaching, has led to the establishment of the series Texts in Applied Mathematics (TAM). The development of new courses is a natural consequence of a high level of excitement on the research frontier as newer techniques, such as numerical and symbolic computer systems, dynamical systems, and chaos, mix with and reinforce the traditional methods of applied mathematics. Thus, the purpose of this textbook series is to meet the current and future needs of these advances and to encourage the teaching of new courses. TAM will publish textbooks suitable for use in advanced undergraduate and beginning graduate courses, and will complement the Applied Mathe- matical Sciences (AMS) series, which will focus on advanced textbooks and research-level monographs. Pasadena, California Providence, Rhode Island College Park, Maryland J.E. Marsden L. Sirovich S.S. Antman

Preface to the Third Edition This edition contains four new sections on the following topics: the BDDC domain decomposition preconditioner (Section 7.8), a convergent adap- tive algorithm (Section 9.5), interior penalty methods (Section 10.5) and p functions (Section 10.6). Poincar´e-Friedrichs inequalities for piecewise W 1 We have made improvements throughout the text, many of which were suggested by colleagues, to whom we are grateful. New exercises have been added and the list of references has also been expanded and updated. Some of the new material originated from our research and we would like to thank the National Science Foundation for support. The ﬁrst au- thor would also like to thank the Alexander von Humboldt Foundation for supporting her visit to Germany in the Summer of 2007, during which the work on this edition was completed. The second author would also like to thank the Universit´e Pierre et Marie Curie for supporting his visits to Paris during the past several years, during which work related to this edition was carried out. In the preface to the ﬁrst edition, we outlined diﬀerent ways the book could be used in courses, but since some chapter numbers have changed, we rephrase these suggestions here. Chapters 0 through 5 form the essential material for a course (these chapter numbers have not changed). Chapters 6 and 7 provide an introduction to eﬃcient iterative solvers for the linear systems of ﬁnite element equations, but they do not contain material re- quired by later chapters. A course emphasizing algorithmic aspects would include them. Similarly, Chapters 8 and 9 are not required in later chapters. A course covering challenging analysis questions would cover these. The for- mer develops and applies max-norm error estimates to nonlinear problems, and the latter introduces the concept of mesh adaptivity. Chapter 10, how- ever, has an essential role in the subsequent chapters. But one could cover only the ﬁrst and third sections of this chapter and then go on to Chapter 11 or 12 to study typical systems of diﬀerential equations found in appli- cations. Chapter 13 is essentially a continuation of Chapter 12. Chapters 10-13 form the core for a course emphasizing basic models in mechanics. Chapter 14 is an independent topic at a somewhat more advanced level that only depends on Chapters 0-5. It develops some functional analysis techniques and their application to ﬁnite element methods. Baton Rouge, LA Chicago, IL 20/07/2007 Susanne C. Brenner L. Ridgway Scott

Preface to the Second Edition This edition contains two new chapters. The ﬁrst one is on the additive Schwarz theory with applications to multilevel and domain decomposition preconditioners, and the second one is an introduction to a posteriori error estimators and adaptivity. We have also included a new section on an ex- ample of a one-dimensional adaptive mesh, a new section on the discrete Sobolev inequality and new exercises throughout. The list of references has also been expanded and updated. We take this opportunity to extend thanks to everyone who provided comments and suggestions about this book over the years, and to the Na- tional Science Foundation for support. We also wish to thank Achi Dosanjh and the production staﬀ at Springer-Verlag for their patience and care. Columbia, SC Chicago, IL 20/02/2002 Susanne C. Brenner L. Ridgway Scott

资料库

The Mathematical Theory of Finite Element Methods.pdf

相关推荐

课程资源

热门标签

最新资料