Finite element methods and their applications

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).