Numerical integration refers to all the procedures, algorithms and techniques in the numerical analysis to obtain an approximate solution to a definite integral.
That is, how to obtain a numerical value of:
where can be a 1D, 2D or 3D domain.
For our interest in the Finite Element Method, the purpose is to describe how the element matrices can be integrated numerically.
Gauss-Legendre Numerical Integration
To fix the most basic concepts on Numerical Integration, we will focus our description on a one dimensional integration using the Gauss-Legendre quadrature, that is, to solve: