Introduction

The finite element method is a numerical technique that gives approximate solutions to differential equations that model problems arising in physics and engineering. In finite difference methods, the mesh consisted of rows and columns of orthogonal lines; in finite elements, each subregion or “element” is unique and need not be orthogonal to the others. In contrast to finite difference procedures, the governing equations in the finite element method are integrated over each finite element, and the contributions summed over the entire problem domain. The history of the finite element method is particularly interesting, especially since the method as such has only been in existence since the mid-1950s. The beginnings of the finite element method actually stem from these early numerical methods and the frustration associated with attempting to use finite difference methods on more difficult, geometrically irregular problems. The chapter also presents an overview of the key concepts discussed in this book.