Let $T$ be a triangle and let $f$ be a smooth function on $T$.We can use mid-point quadrature $\int f dx \approx |T|\cdot f(x_M)$, where $x_M$ is the middle-point of $T$.Can you provide me with (a reference for) higher-order formulas on a simplex?
Higher-order numerical integration on a triangle/tetrahedron/simplex
quadrature
Is it important to have the most efficient rules possible? Do you require all weights to be positive and/or all points to be inside the region? Two general resources:The Encyclopaedia of Cubature Formulas and referenced papers.The Libmesh source contains good choices of cubature rules for all orders, with and without negative weights, thanks to John Peterson. An example src/quadrature/quadrature_gauss_3D.C