The Mathematical Theory of Finite Element Methods
Authors: Brenner, Susanne, Scott, Ridgway
Free Preview- A rigorous and thorough mathematical introduction to the foundations of the subject
- A clear and concise treatment of modern fast solution techniques
- Third edition substantially updated with new material on Additive Schwarz Preconditioners and Adaptive Meshes
- Adaptable text that can be used in the context of differing course paths
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- About this Textbook
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This book develops the basic mathematical theory of the finite element method, the most widely used technique for engineering design and analysis.
The third edition contains four new sections: the BDDC domain decomposition preconditioner, convergence analysis of an adaptive algorithm, interior penalty methods and Poincara\'e-Friedrichs inequalities for piecewise W^1_p functions. New exercises have also been added throughout.
The initial chapter provides an introducton to the entire subject, developed in the one-dimensional case. Four subsequent chapters develop the basic theory in the multidimensional case, and a fifth chapter presents basic applications of this theory. Subsequent chapters provide an introduction to:
- multigrid methods and domain decomposition methods
- mixed methods with applications to elasticity and fluid mechanics
- iterated penalty and augmented Lagrangian methods
- variational "crimes" including nonconforming and isoparametric methods, numerical integration and interior penalty methods
- error estimates in the maximum norm with applications to nonlinear problems
- error estimators, adaptive meshes and convergence analysis of an adaptive algorithm
- Banach-space operator-interpolation techniques
The book has proved useful to mathematicians as well as engineers and physical scientists. It can be used for a course that provides an introduction to basic functional analysis, approximation theory and numerical analysis, while building upon and applying basic techniques of real variable theory. It can also be used for courses that emphasize physical applications or algorithmic efficiency.
Reviews of earlier editions: "This book represents an important contribution to the mathematical literature of finite elements. It is both a well-done text and a good reference." (Mathematical Reviews, 1995)
"This is an excellent, though demanding, introduction to key mathematical topics in the finite element method, and at the same time a valuable reference and source for workers in the area."
(Zentralblatt, 2002)
- Reviews
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Second Edition
S.C. Brenner and L.R. Scott
The Mathematical Theory of Finite Element Methods
"[This is] a well-written book. A great deal of material is covered, and students who have taken the trouble to master at least some of the advanced material in the later chapters would be well placed to embark on research in the area."
ZENTRALBLATT MATH
From the reviews of the third edition:
"An excelent survey of the deep mathematical roots of finite element methods as well as of some of the newest and most formal results concerning these methods. … The approach remains very clear and precise … . A significant number of examples and exercises improve considerably the accessability of the text. The authors also point out different ways the book could be used in various courses. … valuable reference and source for researchers (mainly mathematicians) in the topic." (Calin Ioan Gheorghiu, Zentralblatt MATH, Vol. 1135 (13), 2008)
- Table of contents (15 chapters)
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Basic Concepts
Pages 1-22
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Sobolev Spaces
Pages 23-47
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Variational Formulation of Elliptic Boundary Value Problems
Pages 49-67
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The Construction of a Finite Element Space
Pages 69-92
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Polynomial Approximation Theory in Sobolev Spaces
Pages 93-127
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Table of contents (15 chapters)
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Bibliographic Information
- Bibliographic Information
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- Book Title
- The Mathematical Theory of Finite Element Methods
- Authors
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- Susanne Brenner
- Ridgway Scott
- Series Title
- Texts in Applied Mathematics
- Series Volume
- 15
- Copyright
- 2008
- Publisher
- Springer-Verlag New York
- Copyright Holder
- Springer-Verlag New York
- eBook ISBN
- 978-0-387-75934-0
- DOI
- 10.1007/978-0-387-75934-0
- Hardcover ISBN
- 978-0-387-75933-3
- Softcover ISBN
- 978-1-4419-2611-1
- Series ISSN
- 0939-2475
- Edition Number
- 3
- Number of Pages
- XVIII, 400
- Topics
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