Overview

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).

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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)

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)

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