Overview

Up to now we have discussed many aspects regarding mesh generation and mesh modification and while our final objective is to provide meshes required for finite element simulations, we have not yet dealt with such methods ^[1] directly.

However, in some parts of the book, we have faced some mesh generation problems where more advanced knowledge about finite elements was necessary to understand what needed to be done (see, for instance, the numbering issues related to finite element nodes in Chapter 17). Also, in later chapters, we will discuss h-methods, p-methods and hp-methods (in terms of meshing technologies) and clearly, at that time, it will be necessary to know more about the corresponding finite element requirements. Thus, covergae of the finite element method appears to be necessary before moving on to further investigations.

Nonetheless, library bookshelves are straining under the weight of literature on finite element theory as well as practical manuals for finite element methods, and it is clearly impossible for this book to compete with such a wealth of specialized literature. Thus, the point of view adopted here will be clearly motivated by the following question: "what must be known about finite elements in order to successfully deal with a meshing problem?".

In what follows, the theoretical point of view is largely based on [Ciarlet-1991] to which the reader is referred for a more advanced view of the problem together with a comprehensive list of relevant references about finite element theory and practice.