ABSTRACT
The most popular numerical method is the finite element method (FEM), and this chapter presents the fundamental aspects involved in it. The FEM has been extensively dealt with in the literature; in addition to numerous articles, a large number of standard texts giving detailed presentation of the method are available. It is a versatile tool that is applied to problems in virtually any field. In general, any physical problem can be described in terms of mathematical expressions—differential equations, integral equations, and algebraic equations, of which differential equations are most common. In the FEM, the domain or the body is divided into a finite number of subdomains that share common edges and are interconnected at certain points. A physical problem is described in terms of a number of field variables—known and unknown. Elements of smaller sizes are needed in areas of rapidly changing geometry, load, and material properties so that body is appropriately represented by the mesh of elements.
