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The Mathematical Theory of Finite Element Methods (Texts in Applied Mathematics) (Englisch) Gebundene Ausgabe – 1. Januar 2008

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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."


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)


This book develops the basic mathematical theory of the finite element method, the most widely used technique for engineering design and analysis. It formalizes basic tools that are commonly used by researchers in the field but not previously published. The book will be 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. Different course paths can be chosen, allowing the book to be used for courses designed for students with different interests.For example, courses can emphasize physical applications, or algorithmic efficiency and code development issues, or the more difficult convergence theorems of the subject. This new edition is substantially updated with additional exercises throughout and new chapters on Additive Schwarz Preconditioners and Adaptive Meshes. "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.

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Amazon.com: 4.0 von 5 Sternen 3 Rezensionen
17 von 17 Kunden fanden die folgende Rezension hilfreich
5.0 von 5 Sternen a nice introductory book 6. April 2000
Von Gabriel Barrenechea - Veröffentlicht auf Amazon.com
Format: Gebundene Ausgabe
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 von 1 Kunden fanden die folgende Rezension hilfreich
5.0 von 5 Sternen Excellent book. 7. Mai 2008
Von Mauricio Osorio - Veröffentlicht auf Amazon.com
Format: Gebundene Ausgabe Verifizierter Kauf
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 von 6 Kunden fanden die folgende Rezension hilfreich
2.0 von 5 Sternen A book for experienced people only. 20. Dezember 2006
Von applied math student - Veröffentlicht auf Amazon.com
Format: Gebundene Ausgabe
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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