An adaptive numerical integration algorithm for polygons

In this paper an adaptive numerical integration algorithm for polygons is constructed by cubatures based on finite quadrilateral elements, with particular reference to an 8-node spline finite element. Some numerical examples are given to evaluate the performance of the proposed algorithm, combined with several cubatures with accuracy of order two. The results are also compared with those obtained by two cubatures based on triangulation and a recent method based on the Greenʹs integral formula and Gaussian rules.