Higher Order Elements
As stated in Section 3.6, the finite element method (FEM) is born when we choose the shape functions in a Galerkin weighted residuals formulation to be defined locally over subdomains of Ω that we identify as elements. In this chapter we will develop families of elements in one and two dimensions and introduce the most basic three-dimensional elements. We will restrict ourselves to the ones applicable to fluid flow and heat transfer. Hence we will not venture into the development of some classes of elements of importance in structural analysis such as C1 and hierarchical elements or hybrid elements. However, occasionally the need arises to construct a special element, and therefore we will include the theory of blending function interpolation, which provides us with an easy method to construct elements with practically any behavior for second-order boundary value problems.