# How are the location of Gausian points determined in Finite element theory?

From the finite element theory, what is remained a bit unclear for me, is that how do we know the location of gausian points where the integration is done for each specific type of element ? it is not indicated in many FEM books, but if someone could explain it here , it would be fantastic

• See en.wikipedia.org/wiki/…. The Gauss points are called Gauss nodes in the article. They are the $i$-th roots of the associated Legendre polynomials in [-1,1]. Isoparametric assumptions are used to convert fom [-1,1] to arbitrary coordinate ranges. Sep 7 '19 at 22:04

## 2 Answers

As far as I know the location of integration points is governed by numerical method used for integration. I know only one method of numerical integration, Gauss Quadrature. For details of Gauss Quadrature, please see Wikipedia article or Introduction to Finite Element Method by J.N. Reddy.

If you are using standard Gauss quadrature, from the formulation, you determine the coefficients (weights of Gauss location) and their locations. You cannot arbitrarily decide their locations. Here are some examples: http://edwilson.org/BOOK-Wilson/G-inter.pdf