ABSTRACT
This chapter presents basic definitions, concepts, and elements of mapping and interpolation. It presents development of higher order global differentiability local approximations for two dimensional quadrilateral elements of distorted geometries in xy-space. The chapter provides derivations of the higher order global differentiability local approximations for distorted quadrilateral elements using a completely different approach. The concept of area coordinates is the most natural way to derive basis functions for triangular elements. "Serendipity" means discovery by chance. Thus, this family of elements has very little theoretical or mathematical basis other than the fact that in generating approximation functions for these elements people only utilize the two fundamental properties of the approximation functions.
