ABSTRACT
Integration over the domain of an element is a necessary step for evaluating the elementary matrix and other relevant vectors. The Gauss quadrature method approximates an integration with the weighted sum of the integrand evaluated at some predetermined locations. This chapter discusses how Gauss quadrature works. The general idea behind Gauss quadrature is to reduce the difficulty level of calculation by expressing integration as a sum of a series of multiplications. The chapter examines integration in a one-dimensional (1D) situation. The Gauss quadrature method for 1D space can be extended to 2D space of quadrilateral shapes by adding a second dimension. The chapter discusses Gauss quadrature for 2D triangular elements and 3D Tetrahedral elements.
