Finite Element Methods And Their Applications

The finite element method is one of the major tools used in the numerical solution of partial differential equations in science and engineering. This book offers a fundamental and practical introduction to this method, its various variants, and their applications. In presenting the material, the author has attempted to introduce every concept in the simplest setting and to maintain a level of treatment that is as rigorous as possible without being unnecessarily abstract. All the three major types of partial differential equations, i.e., elliptic, parabolic, and hyperbolic equations, are treated in this book. Nonlinear problems are studied as well. Furthermore, there are four chapters on applications of the finite element method to solid and fluid mechanics, multiphase flows in porous media, and semiconductor modelling. The book contains unique recent developments of various finite elements such as nonconforming, mixed, discontinuous, characteristic, and adaptive finite elements, along with their applications.