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An Introduction to the Mathematical Theory of Finite Elements |  |
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An Introduction to the Mathematical Theory of Finite Elements | |
This introduction to the theory of Sobolev spaces and Hilbert space methods in partial differential equations is geared toward readers of modest mathematical backgrounds. It offers coherent, accessible demonstrations of the use of these techniques in developing the foundations of the theory of finite element approximations.
J. T. Oden is Director of the Institute for Computational Engineering & Sciences (ICES) at the University of Texas at Austin, and J. N. Reddy is a Professor of Engineering at Texas A&M University. They developed this essentially self-contained text from their seminars and courses for students with diverse educational backgrounds. Their effective presentation begins with introductory accounts of the theory of distributions, Sobolev spaces, intermediate spaces and duality, the theory of elliptic equations, and variational boundary value problems. The second half of the text explores the theory of finite element interpolation, finite element methods for elliptic equations, and finite element methods for initial boundary value problems. Detailed proofs of the major theorems appear throughout the text, in addition to numerous examples.
网友对An Introduction to the Mathematical Theory of Finite Elements的评论
该书是挺不错的，很喜欢。
I like this book.
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).
Very good to understand the mathematical principles of the Finite Element Method
The author of this book is a great cintifico profound knowledge of the theory of finite elements. I use it in research work in Mathematics.
Thanks
Marcos
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