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The Mathematical Theory of Finite Element Methods (Texts in Applied Mathematics), by Susanne Brenner, Ridgway Scott
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This is the third and yet further updated edition of a highly regarded mathematical text. Brenner develops the basic mathematical theory of the finite element method, the most widely used technique for engineering design and analysis.
- Sales Rank: #2896510 in Books
- Published on: 2010-11-29
- Released on: 2010-11-29
- Original language: English
- Number of items: 1
- Dimensions: 9.00" h x .95" w x 6.00" l, 1.29 pounds
- Binding: Paperback
- 400 pages
From the Back Cover
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)
Review
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)
Most helpful customer reviews
17 of 17 people found the following review helpful.
a nice introductory book
By Gabriel Barrenechea
This book is a very nice introductory book on the subject. It has a very nice presentation of the fundamental issues on finite element theory, such as interpolation theory on Sobolev spaces and variational formulations of elliptic problems. Also, it covers some advanced and more specific subjets such as multigrid methods and mixed methods for fluid mechanics, where it reviews some of the most used techniques to solve the saddle-point problems such as Augmented Lagrangian techniques and penalty methods.
Also, at the end of the book there is a very well written chapter focused on Interpolation operators, where there is a very nice (and very easy to read) presentation of the Sccot-Zhang interpolation operator, and some of the principal results on approximation.
Resuming, it is a very recomendable book in the subjet, specially recomendable for mathematics students interested on finite elements, and researchers in the field.
1 of 1 people found the following review helpful.
Excellent book.
By Mauricio Osorio
This is an excellent book to learn about the mathematical foundations of FEM. It is good not only for advanced (graduate) students but also the author gets to try the topic in a manner understandable also for less-expert students or researchers.
2 of 6 people found the following review helpful.
A book for experienced people only.
By applied math student
This book certainly has a lot of information in it, but it is not lucid at all. This book is a hard read. The presentation is not done very well, and a lot of details get put off to the literature. I would actually recommend the FEM book by Braess instead. Only use this book as a reference.
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