Basic Concepts

The finite element method provides a formalism for generating discrete (finite) algorithms for approximating the solutions of differential equations. It should be thought of as a black box into which one puts the differential equation (boundary value problem) and out of which pops an algorithm for approximating the corresponding solutions. Such a task could conceivably be done automatically by a computer, but it necessitates an amount of mathematical skill that today still requires human involvement. The purpose of this book is to help people become adept at working the magic of this black box. The book does not focus on how to turn the resulting algorithms into computer codes, although this is at present also a complicated task. The latter is, however, a more well-defined task than the former and thus potentially more amenable to automation.