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An Introduction to the Mathematical Theory of Finite Elements (Dover Books on Engineering) Paperback – March 23, 2011
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Top Customer Reviews
This book is about Functional Analysis, Distribution Theory and Sobolev Spaces applied to Partial Differential Equations. That's what Finite Elements is all about.
Most of the Finite Elements' books are very approached only to Engineering students, but this book approaches both Engineers and Mathematicians.
I think this book is a great theoretical complement to other Finite Element books, and this book is very cheap, thus it's worth the price!
The first chapters are all about Distribution Theory and Sobolev Spaces. The next chapters presents Finite Elements in the context of the different types of Partial Differential Equations that the methods can be applied.
There are other great books like the Sobolev Spaces by Robert Adams and John Fournier, as well as the Partial Differential Equations by Lawrence Evans, which treat these subjects in more details. But I think this book suffices in explaining those subjects because it is self contained.
This book includes a treatment of Finite Elements applied to Transient Problems like the Diffusion and/or Heat Equation, and some Variational Principles. It also includes formulations for other types of PDEs.
I consider that the level of difficulty is Medium to High, or Advanced. I like the chapters on Distribution Theory and Sobolev Spaces.
I recommend this book to mathematicians who wants to learn the Finite Element Methods from an Abstract Point of view, and to Advanced Engineers (Elevés).