ABSTRACT
This chapter discusses The finite element method is indeed one such method that permits us to satisfy all of the above requirements. In applying the finite element method for approximating solutions of BVPs, one must adhere to the following basic steps regardless of the type of operator and the method of approximation used in constructing the integral form. Thus, the finite element method can be thought of as piecewise (a piece being a subdomain or a finite element) application of classical methods of approximation. This is the fundamental difference between classical methods of approximation and the finite element method. In the finite element mesh, the nodes and the elements are uniquely numbered. The choice of numbers for the nodes is irrelevant as long as they are unique. The end result of discretization is that we have a finite element mesh with M elements and N nodes clearly identified.
