An Introduction to the Mathematical Theory of Finite Elements (Dover Books on Engineering) by J. T. Oden (PDF)

Description

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.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐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).

⭐This is one of the best mathematical textbooks on FEM. If you are interested on approximation, estimates, and the most useful tools of functional analysis used in the FEM formulations then you should get this book. On the other hand, if you are more interested on computer implementation, linear solvers, and specific applications problems (elasticity, fluid dynamics, etc) then there are better choices, but even in this case it would be a good idea to have a copy of this book. This text was first published by wiley, a hard cover and expensive edition, so this dover’s edition is very welcome.

⭐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.ThanksMarcos

⭐inklusive der Distributionentheorie und der Sobolev-Räume, findet man in diesem Klassiker aus den 1970er Jahren. Dem Vorwort zufolge ist das Buch (auch) für Studierende des Ingenieurwesens konzipiert, aber das ist schwer vorstellbar. Die gesamte erste Hälfte des Buches besteht aus Mathematik – reelle und Funktionalanalysis – bevor man überhaupt zu den etwas praktischeren Fragen der FEM kommt. Wie auch den Klassiker von Dietrich Braess

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

⭐habe ich dieses Buch genossen und viel daraus gelernt, als ich es noch als Student in die Finger bekam. Es ist Dover zu verdanken, dass es nun äußerst preiswert wieder vorliegt.

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⭐Para los interesados en el elemento finito, es obligado comenzar con este título, da las bases para abordar los otros títulos del autor

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⭐Muito útil para um estudo teórico inicial e intermediário a respeito do método dos elementos finitos.

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