ABSTRACT
This chapter presents basic definitions, concepts and details of interpolation theory and mapping. This material is an integral component of the finite element method and allows one to map irregular element shapes into standard shapes to evaluate the integrals as well as permits construction of local approximation functions. In two dimensions, the element geometry may be of triangular shape or of quadrilateral shape with straight or curved sides. Such distorted irregular shapes present difficulty when performing integration over the area of the element for calculating coefficients of the element matrices and vectors. Another difficulty that is much more significant is the construction of local approximation functions for quadrilateral and irregular shapes. The concept of area coordinates is the most natural way to derive basis functions for triangular elements. Consider a three node triangular element with straight sides. Provide program listing, results, tables and plots along with a write-up on the equations used as part of the report.
