Several new quadrature formulas for polynomial integration in the triangle

Details Several new quadrature formulas for polynomial integration in the triangle Several new quadrature formulas for polynomial integration in the triangle

2005-01-27

arxiv.org/abs/math/0501496v2

Mathematics

Numerical Analysis

14 pages, 14 figures, 5 pages of tabulated quadrature points. Correct reference

Scientific paper

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.

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