A new 11 point degree 6 cubature formula for the triangle

We present a new cubature formula in the triangle which exactly integrates polynomials up to degree 6, using only 11 points. The formula was computed by starting with a 12 point cubature formula and applying the reduced basis method to drive one of the weights to zero, resulting in an 11 point formula with positive weights and no points outside the triangle. This improves upon the previously best known positive inside formulas, which have 12 or more points. The lower bound on the number of points for a degree 6 cubature formula in the triangle is 10, which to date has only been obtained by allowing some of the points to be outside the triangle. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)