Introduction

In the last two lectures, we developed the finite element formulation of a typical 2-D problem using the simplest triangular element. This triangular element has 3 nodes and the corresponding shape functions are linear. Since the degree of freedom per node is one, this element is called as the Lagrangian triangular element, or to be precise, first order Lagrangian triangular element. The corresponding shape functions are called as Lagrangian shape functions and the approximation is called as Lagrangian approximation. Thus, equations (21.6) or (21.12) represent the first order or linear Lagrangian shape functions and equation (21.5) represents the first order or linear Lagrangian approximation.

In this lecture, we shall develop the higher order Lagrangian triangular elements using the approximation of order higher than linear.