Finite Elements: An Introduction to the Method and Error Estimation PDF

Preface

There are many mathematical and engineering books on the finite element method and, at a recent count, more than 200 000 papers addressing finite elements and their applications; (for details of the annual count over the last 40 years see, e.g., the website of Jaroslav Mackerle). One has therefore to ask the questions ‘Why write yet another book on the finite element method, what is the philosophy and what are the aims that justify another book, and what is the audience for the book?'

In spite of the existence of the large number of finite element books, it can be said that they are all in the main devoted primarily either to the mathematical theory of finite element methods, or to engineering applications, but usually not to both. So, in response to the above questions we feel that there is a need for a book that presents the main theoretical ideas of the finite element method and the analysis of its errors in an accessible way, and that demonstrates the interrelationship between the theory and the computed numbers. The book should show how the theory contributes to the understanding of computed results and builds confidence in the method and the correctness of a finite element program. Further, the book should require the minimum of pre-requisites for understanding the basic theory presented, it should as far as possible be self-contained, and it should address questions that are relevant to numerical methods for partial differential equations. Finally, it should address the numerical computation of typical simple engineering problems, showing the numerical features, analysing them, explaining them and drawing conclusions.