Ebook: A concise overview of the finite element method

This is the third book in a series designed to make the finite element method and adaptive refinement more accessible. The first book, A Unified Approach to the Finite Element Method and Error Analysis Procedures, laid the theoretical background for simplifying and extending the finite element and finite difference methods by introducing the use of a physically interpretable notation. This notation simplifies and extends computational mechanics by reversing the usual mathematical approach of abstracting the notation used in the development. By introducing variables that represent rigid body motions and strain quantities, the modeling capabilities of individual elements and the solution algorithms can be evaluated for accuracy by visual inspection. The second book, The Essentials of Finite Element Modeling and Adaptive Refinement, demonstrated the validity of the derivations contained in the first book and extended the simplification of element formulation and improved the error measures. This book, as its title indicates, presents a straightforward introduction to the finite element method, error analysis, and adaptive refinement. As such, it provides an easy-to-read overview that allows the contents of other finite element books and finite element courses to be seen in perspective as the various procedures are encountered. Furthermore, it provides developments that improve the procedures contained in the standard finite element textbook. As a result, when this book is used alone or in conjunction with other presentations, the reader is capable of critically assessing the capabilities of the finite element method. Read more...