Theory and Practice of Finite Elements
Authors: Ern, Alexandre, Guermond, JeanLuc
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 About this Textbook

This book presents the mathematical theory of finite elements, starting from basic results on approximation theory and finite element interpolation and building up to more recent research topics, such as and Discontinuous Galerkin, subgrid viscosity stabilization, and a posteriori error estimation.
The body of the text is organized into three parts plus two appendices collecting the functional analysis results used in the book. The first part develops the theoretical basis for the finite element method and emphasizes the fundamental role of infsup conditions. The second party addresses various applications encompassing elliptic PDE's, mixed formulations, firstorder PDEs, and the timedependent versions of these problems. The third part covers implementation issues and should provide readers with most of the practical details needed to write or understand a finite element code.
Written at the graduate level, the text contains numerous examples and exercises and is intended to serve as a graduate textbook. Depending on one's interests, several reading paths can be followed, emphasizing either theoretical results, numerical algorithms, code efficiency, or applications in the engineering sciences.
The book will be useful to researchers and graduate students in mathematics, computer science and engineering.
 Reviews

From the reviews:
"This book represents an excellent compendium of information about the mathematics and numerical analysis of the finite … . Its userability, for the writing … is guaranteed through the inclusion of a discussion … . will be a useful text for advanced mathematics/engineering graduates who wish to learn about … good background information for the engineer who will eventually apply the finite element method to practical realworld problems. In addition, it will be an excellent text for the mathematics graduate … . (R.S.Anderssen, Mathematical Reviews, 2005)
"This book is an expanded version of Lecture Notes published by the authors in French … . It has been used as a textbook for graduate finite element courses … . The book can be used in several courses in Mathematics, Computer Science, and Engineering programs. The authors offer suggestions for course titles and syllabi. … The book is organized into three parts. … Many bibliographic entries to the extensive literature on finite elements are given throughout the book." (I.N. Katz, Zentralblatt Math, Vol. 1059 (10), 2005)
"A relative complete coverage of issues concerning finite element methodology based soundly on theory. … this is a selfcontained presentation which goes relatively far regarding the questions of stability, approximation and error estimation and demonstrates the use of the rather abstract concepts in concrete situations. The presentation is suited for the mathematician and also for applied scientists should they be ready to digest the more abstract concepts which, however, prove very useful understanding how to obtain a working code for the problem at hand." (H. Muthsam, Monatshefte für Mathematik, Vol. 148 (2), 2006)
"Overall, the authors have largery succeeded in giving a rather comprehensive exposition of the finite element method and its challenges, up to some current research topics, in less than 500 pages, yet without taking any unreasonable shortcut, by no means an easy task."
(SIAM Review)
 Table of contents (10 chapters)


Finite Element Interpolation
Pages 380

Approximation in Banach Spaces by Galerkin Methods
Pages 81108

Coercive Problems
Pages 111174

Mixed Problems
Pages 175217

FirstOrder PDEs
Pages 219278

Table of contents (10 chapters)
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Bibliographic Information
 Bibliographic Information

 Book Title
 Theory and Practice of Finite Elements
 Authors

 Alexandre Ern
 JeanLuc Guermond
 Series Title
 Applied Mathematical Sciences
 Series Volume
 159
 Copyright
 2004
 Publisher
 SpringerVerlag New York
 Copyright Holder
 Springer Science+Business Media New York
 eBook ISBN
 9781475743555
 DOI
 10.1007/9781475743555
 Hardcover ISBN
 9780387205748
 Softcover ISBN
 9781441919182
 Series ISSN
 00665452
 Edition Number
 1
 Number of Pages
 XIV, 526
 Topics