ABSTRACT
It is customary to start any presentation on finite elements with onedimensional elliptic problems. In this opening chapter, we will study a model two-point elliptic boundary value problem (BVP) for a linear differential equation of second order. We shall discuss the equivalence of classical and variational formulations, equivalence with a minimization problem, and then follow in the next chapters with foundations of the Galerkin method, and a development of a 1D hp code. Much of the introduced formalism will seem to be over-sophisticated as it is motivated with the anticipated development of related ideas in two and three space dimensions.
