Several new quadrature formulas for polynomial integration in the triangle

Mark A. Taylor, Beth A. Wingate, Len P. Bos

Published 2005-01-27, updated 2007-02-08Version 2

We present several new quadrature formulas in the triangle for exact integration of polynomials. The points were computed numerically with a cardinal function algorithm which imposes that the number of quadrature points $N$ be equal to the dimension of a lower dimensional polynomial space. Quadrature forumulas are presented for up to degree $d=25$, all which have positive weights and contain no points outside the triangle. Seven of these quadrature formulas improve on previously known results.