Several new quadrature formulas for polynomial integration in the triangle

• DOI: 10.48550/arxiv.math/0501496
• Publication Date: 2005-01-01
• Authors: Taylor, Mark A.; Wingate, Beth A.; Bos, Len P.
• Keywords: 65D30 (Secondary), 65D32 (Primary), 65M60, 65M70, 41A10; FOS: Mathematics; Mathematics - Numerical Analysis; Numerical Analysis (math.NA); 0101 mathematics; 01 natural sciences

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.<br/>14 pages, 14 figures, 5 pages of tabulated quadrature points. Correct reference<br/>