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Numerical Solution of Partial Differential Equations by the Finite Element Method [Paperback]

Claes Johnson
4.0 out of 5 stars  See all reviews (2 customer reviews)
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Book Description

Jan. 15 2009 048646900X 978-0486469003
An accessible introduction to the finite element method for solving numeric problems, this volume offers the keys to an important technique in computational mathematics. Suitable for advanced undergraduate and graduate courses, it outlines clear connections with applications and considers numerous examples from a variety of science- and engineering-related specialties.This text encompasses all varieties of the basic linear partial differential equations, including elliptic, parabolic and hyperbolic problems, as well as stationary and time-dependent problems. Additional topics include finite element methods for integral equations, an introduction to nonlinear problems, and considerations of unique developments of finite element techniques related to parabolic problems, including methods for automatic time step control. The relevant mathematics are expressed in non-technical terms whenever possible, in the interests of keeping the treatment accessible to a majority of students.

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Customer Reviews

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Most helpful customer reviews
By Gaia
This is a much needed re-print of one of the great classics on the Finite Element Method. It combines simplicity and clarity and is indispensable for the beginning graduate level.
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3.0 out of 5 stars Good contents, bad presentation June 11 2011
By Phollox
The content of this book is fairly complete. But the treatment of each subject is not very detailed. So you end up with a 288 pages book which deals with the same amount of content that the Zienkiewicz & Taylor. And I really don't like the typesetting
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Most Helpful Customer Reviews on Amazon.com (beta)
Amazon.com: 4.4 out of 5 stars  9 reviews
15 of 15 people found the following review helpful
5.0 out of 5 stars Best book on mathematics of FEM June 20 2010
By A. I. Haque - Published on Amazon.com
This book provides an excellent mathematical introduction to the Finite Element Method. All of the necessary functional analysis concepts are provided. This book is aimed at mathematicians and not engineers!

Cautionary notes:
1. A strong background in mathematical analysis is required to understand the proofs.
2. Few implementation details provided.
3. Focus is primarily on elliptic PDEs. Only 1 chapter each for Parabolic and Hyperbolic PDEs.

This was the textbook I had for a grad math course in FEM. I had previously studied FEM on my own through an engineering text. Engineering FEM books explain FEM through a bottom-up approach: formulating the elements and then assembling them. Mathematical FEM books explain FEM through a top-down approach: formulating the solution space and then specifying the elements. This book follows the mathematical approach, so you will not find it useful in terms of implementation or applications. However, the proofs are fairly easy to follow (for a mathematician).
6 of 6 people found the following review helpful
5.0 out of 5 stars Among the best introduction to FEM Oct. 7 2010
By Luciano Teresi - Published on Amazon.com
I am dealing with FEM since many years, and in many ways. I use FEM as a computational tool, I teach FEM at graduate level, and I am involved in developing new computational tools related to FEM.

Among the many books devoted to the subject, that by C. Johnson is definitely one of the best; my opinion is that no other book can introduce you to the method as seamlessly, yet accurately, as this book does. I strongly suggest the book to anyone interested in the subject. Despite its age (first published in 1987), it is still extremely useful.
5 of 5 people found the following review helpful
5.0 out of 5 stars Very good Nov. 7 2010
By Vedran Jagodnik - Published on Amazon.com
Format:Paperback|Verified Purchase
I bought this book for my phd course. Although the book is written on a pure mathematical way (and I'm not an mathematician) I did understand almost everything. Nevertheless, before starting to read this you should have in your mind that you NEED to have some basic of advanced mathematics.
I would recommend this book to engineers who are starting to use FEM analysis, and graduate students who are learning the basics of FEM.
4 of 4 people found the following review helpful
3.0 out of 5 stars chapters 1-5 are a good introduction to FEM June 2 2013
By L. de Vito - Published on Amazon.com
At least chapters 1-5 make it a good introductory book. Chapters 6-13 are not so well-written, not so clear: The author goes way too fast and included advanced materials. It would have been better to stay at an introductory level and to further trim it down. It cannot claim 5 stars because of numerous weaknesses:
- as already observed by another reviewer, it is typed in something like Word instead of Latex, hence reading lots of equations is a painful experience !
- it is light on discontinuous Galerkin method and heavy on the streamline diffusion method since the latter was the most promising method at the time this little book was written; since then, the streamline diffusion method is dead and the discontinuous Galerkin method is the standard FE extension to deal with hyperbolic system of equations.
If it does not suffice:
- no Matlab / Octave source code to illustrate
- no errata
- no solution to the exercises
either in the book or on the author's home page.
Nevertheless, at this very low price, I would recommend it for a concise introduction.
5.0 out of 5 stars Great Overview June 12 2014
By Michael Harmon - Published on Amazon.com
This book is a gem. Slightly out of date, but really informative. It covers a lot of material in a more of an overview way, lightly touching on each topic. It is not a book about how to do FEM from an engineering or computational way, more in the mathematical light. In that sense its definitely a great 2nd book on FEM or as a reference on FEM. Even though it is now almost 30 years old a lot of it is still relevant today and its interesting to see a time capsule of where FEM stood and was going at that time. My only complaint is the font, however you get used to that after a little while.
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