A First Example

Abstract

In Chap. 1, we explained the fundamental philosophy that underpins the finite element method—that is, the region on which a differential equation is defined is partitioned into smaller regions known as elements, and the solution on each of these elements is approximated using a low-order polynomial function. In this chapter, with the aid of a simple example, we illustrate how this may be done. This overview will require the definition of some terms that the reader may not be familiar with, as well as a few technical details. We will, however, undertake to keep these definitions to a minimum and will focus on the underlying strategy of applying the finite element method without getting bogged down by these technical details. As a consequence, we will inevitably skate over some mathematical rigour, but will make a note to return to these points in later chapters.