Finite Element Methods and Their Applications (Scientific Computation)

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).

This book serves as a text for one- or two-semester courses for upper-level undergraduates and beginning graduate students and as a professional reference for people who want to solve partial differential equations (PDEs) using finite element methods. The author has attempted to introduce every concept in the simplest possible setting and maintain a level of treatment that is as rigorous as possible without being unnecessarily abstract. Quite a lot of attention is given to discontinuous finite elements, characteristic finite elements, and to the applications in fluid and solid mechanics including applications to porous media flow, and applications to semiconductor modeling. An extensive set of exercises and references in each chapter are provided.