ABSTRACT
In the first chapter, we introduce the theoretical notions and practical concepts underlying the finite element method in one dimension by discussing the numerical solution of the steady diffusion equation in the presence of a distributed source. We begin by addressing the simplest implementation of the finite element method where the solution domain is divided into a number of intervals, called finite elements, and a function of interest is approximated with a linear function over each element. The union of the linear element functions provides us with a continuous, piecewise linear function representing a known or requisite field. Implementations for quadratic and high-order element functions arise as straightforward extensions of the basic formulation. Further applications of the finite element method in one dimension are discussed in Chapter 2.
