Finite Elements: Theory, Fast Solvers, and Applications in Solid Mechanics

Finite Elements: Theory, Fast Solvers, and Applications in Solid Mechanics

By addebook • Jul 3rd, 2008 • Category: Mathematics

Finite Elements: Theory, Fast Solvers, and Applications in Solid Mechanics

Finite Elements: Theory, Fast Solvers, and Applications in Solid Mechanics
By Dietrich Braess
Publisher: Cambridge University Press
Number Of Pages: 384
Publication Date: 2007-04-30
ISBN-10 / ASIN: 0521705185
ISBN-13 / EAN: 9780521705189
Binding: Paperback

This definitive introduction to finite element methods has been thoroughly updated for a third edition which features important new material for both research and application of the finite element method. The discussion of saddle-point problems is a highlight of the book and has been elaborated to include many more nonstandard applications. The chapter on applications in elasticity now contains a complete discussion of locking phenomena. The numerical solution of elliptic partial differential equations is an important application of finite elements and the author discusses this subject comprehensively. These equations are treated as variational problems for which the Sobolev spaces are the right framework. Graduate students who do not necessarily have any particular background in differential equations, but require an introduction to finite element methods will find this text invaluable. Specifically, the chapter on finite elements in solid mechanics provides a bridge between mathematics and engineering.

Summary: A decent introduction to theory and methods for FEM
Rating: 4

I would say I mostly agree with the previous reviewer. The description is pretty clear, despite being a translation, and it has actually proven useful to me during my time in grad school. One minor complaint I have is that some of the proofs he gives are not as clear as I would like them to be. Specifically, I am talking about the sections dealing with the INF-SUP condition. It seems that everyone who writes an FEM book either skirts this whole issue of the INF-SUP condition (which is what a lot of engineering texts do), or they just copy the ’standard’ proofs, which suck. But other than that, this is a useful book to have.

Summary: A Good Book To Learn Finite Elements From
Rating: 4

I recently read this book as part of an advanced numerical analysis class in grad school. I found it to be well written and easy to read. It was useful to me in learning about finite elements from both an abstract and practical perspective. I would recommend it to anyone familiar with the concept of a weak solution to an elliptic partial differential equation and with some experience with numerical linear algebra.
This book could have been improved by including some code or pseudo-code to help get novices started. This is not too severe of a drawback since the text is so well written that the reader should be able to implement many of the ideas without any other training in this area.

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