Finite Element Methods and Their Applications [Paperback]

Introduce every concept in the simplest setting and to maintain a level of treatment that is as rigorous as possible without being unnecessarily abstract.

Contains unique recent developments of various finite elements such as nonconforming, mixed, discontinuous, characteristic, and adaptive finite elements, along with their applications.

Describes unique recent applications of finite element methods to important fields such as multiphase flows in porous media and semiconductor modelling.

Treats the three major types of partial differential equations, i.e., elliptic, parabolic, and hyperbolic equations.

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 ChaplC.