An explicit construction of interpolation nodes on the simplex

An open question concerns the spatial distribution of nodes that are suitable for high-order Lagrange interpolation on the triangle and tetrahedron. Several current methods used to produce nodal sets with small Lebesgue constants are recalled. A new approach is presented for building nodal distributions of arbitrary order, that is based on curvilinear finite-element techniques. Numerical results are shown which demonstrate that, despite the explicit nature of this construction, the resulting node sets are well suited for interpolation and competitive with existing sets for up to tenth-order polynomial interpolation. Matlab scripts which evaluate the node distributions on the equilateral triangle are included.