Zhangxin Chen Knihy

The finite element method is a key tool in numerically solving partial differential equations. This book provides a fundamental and practical introduction to the method, its variants, and applications. Concepts are introduced in a straightforward manner while maintaining rigorous treatment without unnecessary abstraction. The content is based on a graduate course taught at Southern Methodist University and has also been used in seminar notes at Purdue University, the University of Minnesota, and Texas A&M University. Additionally, it served as the foundation for summer schools on the finite element method and its applications in various countries, including China, Iran, Mexico, and Venezuela. The book covers six major topics and four applications. Chapter 1 introduces the standard (H- and H²-conforming) finite element method. Chapters 2 and 3 discuss closely related methods: the nonconforming and mixed finite element methods. Chapters 4 and 5 focus on the recently developed discontinuous and characteristic finite element methods. Chapter 6 examines the adaptive finite element method. The final chapters apply these methods to solid mechanics (Chapter 7), fluid mechanics (Chapter 8), fluid flow in porous media (Chapter 9), and semiconductor modeling (Chapter 10).

Focusing on the finite element method, this book provides a comprehensive introduction to its variants and applications in various engineering fields. Concepts are presented clearly and rigorously, covering one, two, and three-dimensional elements and their use in solving different types of equations and mechanics problems. It includes discussions on control volume and adaptive methods, alongside illustrative computer programs in Fortran and C++. An extensive set of exercises enhances learning, making it suitable for both students and professionals in related fields.

The need to predict, understand, and optimize complex physical and c- mical processes occurring in and around the earth, such as groundwater c- tamination, oil reservoir production, discovering new oil reserves, and ocean hydrodynamics, has been increasingly recognized. Despite their seemingly disparate natures, these geoscience problems have many common mathe- tical and computational characteristics. The techniques used to describe and study them are applicable across a broad range of areas. The study of the above problems through physical experiments, mat- matical theory, and computational techniques requires interdisciplinary col- boration between engineers, mathematicians, computational scientists, and other researchers working in industry, government laboratories, and univ- sities. By bringing together such researchers, meaningful progress can be made in predicting, understanding, and optimizing physical and chemical processes. The International Workshop on Fluid Flow and Transport in Porous - dia was successfully held in Beijing, China, August 2{6, 1999. The aim of this workshop was to bring together applied mathematicians, computational scientists, and engineers working actively in the mathematical and nume- cal treatment of ?uid ?ow and transport in porous media. A broad range of researchers presented papers and discussed both problems and current, state-of-the-art techniques.