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Understanding And Implementing the Finite Element Method
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If you are more mathematically inclined, I would say start with this book before you delve into the gems by Ciarlet The Finite Element Method for Elliptic Problems (Classics in Applied Mathematics) or Brenner and Scott The Mathematical Theory of Finite Element Methods (Texts in Applied Mathematics). As one of the other reviewers mentioned, the theory part of the book is crammed together and kind of lax; well, to me, this would be the perfect place to start into the theory. He covers most of the relevant theory without bogging you down with the technical details to be 100% correct. In a first pass through learning the theory, you probably don't need to be inundated with all of the finer points of Hilbert spaces.
Download the MATLAB code for the book and read through it as you work your way through the book. Gockenbach's discussion of "implementing" the finite element method is very mathematical and not very practical (I don't know why I was expecting anything else from a SIAM book). Examining the code is where you will learn how to implement FEA on your own; the book alone is not sufficient. Better yet, pick up the Cook book ...Read more ›
Also I feel it is lacking enough examples to illustrate his points.
There are lot of theorems , and terminologies, but they are not highlighted , and if you dont use a highlighter of your own, you might spend a lot of time, looking for what a term means when you come accross it sometime later while reading the book.