Chapter 9 - GENERAL INTERPOLATION

Abstract

This chapter provides an overview of general interpolation. In a one-dimensional problem, it does not make a great deal of difference if one selects a local or global coordinate system for the interpolation equations, because the inter-element continuity requirements are relatively easy to satisfy. That is not true in higher dimensions. To obtain practical formulations, it is almost essential to utilize local coordinate interpolations. Doing this requires a small amount of additional work in relating the derivatives in the two coordinate systems. The chapter presents some of the procedures for deriving the interpolation functions in unit coordinates. It illustrates the Serendipity interpolation functions for quadrilateral elements that can be either, linear, quadratic, or cubic on any of its four sides. Such an element is often referred to as a transition element. The chapter also discusses hierarchical interpolation and quadrilateral elements or the quadrilateral faces of a solid element.