Introduction

For computer implementation of the finite element method, the integration involved in the element stiffness matrix and the element force vector needs to be done numerically. Typical numerical integration formulas are available for the master element, i.e., the standard element of size two. In the last lecture, we discussed the mapping function that maps an arbitrary - sized element to the master element. We also transformed the expressions for the element stiffness matrix and the element force vector into the integrals over the master element. In this lecture, we shall discuss how to evaluate these integrals numerically. Before that, we discuss the Gauss quadrature rule, which is the commonly used numerical integration scheme in finite element method. This rule is presented in section 12.1.