Introduction

In its current form the finite element method was formalized by civil engineers. For stress analysis of modern framed structures in civil engineering classically, methods such as slope deflection and moment distribution were used. The structure was divided into component elements, each component was examined separately, and stiffness properties were established. Although a system or a thing could be discretized in smaller systems, components, or finite elements, one must realize that the original system itself is indeed a whole. The foregoing offers a rather abstract description of ideas underlying the process of discretization, inherent in almost all human endeavors. Discretization implies approximation of the real and the continuous. The chapter considers a number of terms to process the scheme of discretization such as subdivision, continuity, compatibility, convergence, upper and lower bounds, stationary potential, minimum residual, and error. Although these terms have specific meanings in engineering applications, their conception has deep roots in man's thinking.