A novel numerical integration technique over arbitrary polygons

In this paper, a new numerical integration technique [1] on arbitrary polygons is presented. The polygonal do- main is mapped conformally to the unit disk using Schwarz-Christoffel mapping [2] and a midpoint quadrature rule defined on the unit circle is used. This method eliminates the need for a two level isoparametric mapping usuall required [3]. Moreover the positivity of the Jacobian is guaranteed. We present numerical results for a few benchmark problems in the context of polygonal finite elements that show the effectiveness of the method