Gauss Legendre quadrature over a triangle

This paper presents a Gauss Legendre quadrature method for numerical int egration over the standard triangular surface: {(x, y) | 0, 1 ,1 } x y xy ≤≤ +≤ in the Cartesian two-dimensional (x, y) sp ace. Mathematical transformation from (x, y) space to ( ξ, η) space map the standard triangle in ( x, y) space to a standard 2-square in ( ξ, η) space: {(ξ, η)|–1 ≤ ξ, η ≤ 1}. This overcomes the difficulties associated with the derivation of new weight coeff icients and sampling points and yields results which are accurate and reliable. Results obtained with new formulae are compared with the existing formulae.