Gauss Legendre:

Efficient usage: 1D (line) elements, 2D quadrilateral elements, 3D hexahedral elements;

Required number of points (Ngp) for a polynomial of degree d:

1D:

Ngp= (d+1)/2

2D:

Ngp(2D)=(Ngp(1D))²

3D:

Ngp(3D)=(Ngp(1D))³