n-dimensional Quadrature

Abstract

This article discusses n‐dimensional quadrature. To show how dimensionality complicates integration rules this article focus on polynomial integration over squares and triangles where quadrature points are required to be on the boundary. In the case of a square, high quality formulae, called Gauss–Lobatto quadrature, are available as tensor products of 1‐dimensional quadrature. In triangles it has been shown that analogous Gauss–Lobatto formulae do not even exist.