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Finite Element Methods and Their Applications

  • Textbook
  • © 2005

Overview

Authors:
  1. Zhangxin Chen

    1. Department of Mathematics, Southern Methodist University, Dallas, USA

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  • As a textbook this is distinctive, if not unique
  • Combines in an elegant way its textbook character and its role as a reference for the practitioner

Part of the book series: Scientific Computation (SCIENTCOMP)

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Table of contents (10 chapters)

  1. Front Matter

    Pages I-XIII
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  2. Elementary Finite Elements

    Pages 1-85

  3. Nonconforming Finite Elements

    Pages 87-116

  4. Mixed Finite Elements

    Pages 117-171

  5. Discontinuous Finite Elements

    Pages 173-213

  6. Characteristic Finite Elements

    Pages 215-259

  7. Adaptive Finite Elements

    Pages 261-304

  8. Solid Mechanics

    Pages 305-320

  9. Fluid Mechanics

    Pages 321-335

  10. Fluid Flow in Porous Media

    Pages 337-362

  11. Semiconductor Modeling

    Pages 363-384

  12. Back Matter

    Pages 385-410
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Keywords

About this book

The ?nite element method is one of the major tools used in the numerical solution of partial di?erential equations. This book o?ers a fundamental and practical introduction to the method, its variants, and their applications. In presenting the material, I have attempted to introduce every concept in the simplest possible setting and to maintain a level of treatment that is as rigorous as possible without being unnecessarily abstract. The book is based on the material that I have used in a graduate course at Southern Methodist University for several years. Part of the material was alsousedformyseminarnotesatPurdueUniversity,UniversityofMinnesota, andTexasA&MUniversity.Furthermore,thisbookwasthebasisforsummer schools on the ?nite element method and its applications held in China, Iran, Mexico, and Venezuela. This book covers six major topics and four applications. In Chap. 1, the 1 2 standard (H-and H -conforming) ?nite element method is introduced. In Chaps.2and3,twocloselyrelated?niteelementmethods,thenonconforming and the mixed ?nite element methods, are discussed. The discontinuous and characteristic?niteelementmethodsarestudiedinChaps.4and5;thesetwo methods have been recently developed. The adaptive ?nite element method is considered in Chap. 6. The last four chapters are devoted to applications of these methods to solid mechanics (Chap. 7), ?uid mechanics (Chap. 8), ?uid ?ow in porous media (Chap. 9), and semiconductor modeling (Chap. 10).

Reviews

From the reviews:

"The attempt to introduce every concept in the simplest possible setting is reflected in the structure of the chapters. … The book and its intention differ very much from the books on finite elements … . The reader finds here more variants of finite element spaces and applications that have not been described in textbooks on finite elements and in particular not with so many details." (Dietrich Braess, Zentralblatt MATH, Vol. 1082, 2006)

"Nowadays, the finite element method is one of the most used in numerical solution of partial differential equations. This book offers a fundamental and practical approach to the method. … In each chapter, a brief introduction, the notation, a basic terminology and necessary concepts are given. Theoretical considerations and bibliographical information are also presented at the end of each chapter. Each of the three main types of partial differential equations is treated in this book. Non-linear problems are studied as well." (Gregory Guisbiers, Physicalia, Vol. 28 (4-6), 2006)

"The book is an excellent written introduction to the fundamentals and the practical application of the finite element method (FEM) and its variants. … Every chapter ends with bibliographical remarks, containing useful sources on the topics, and with a number of meaningful exercises, which complement the presentation. … The book can be used for graduate and even undergraduate courses designed for students with different interests. It is a good reference book for mathematicians, engineers and scientists interested in numerical investigation of mathematical models." (Stefka N. Dimova, Mathematical Reviews, Issue 2006 d)

Authors and Affiliations

  • Department of Mathematics, Southern Methodist University, Dallas, USA

    Zhangxin Chen

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