Higher-order H1-conforming hierarchical basis functions for triangles and tetrahedra

This data set contains H1-conforming basis functions for triangular and tetrahedral finite elements. They are hierarchical in terms of the polynomial order and feature symmetries in terms of barycentric coordinates. Moreover, they are pairwise orthogonal with respect to the interpolation operator. The resulting element matrices exhibit high levels of sparsity and moderate condition numbers in the higher-order case. The functions are given in terms two different formats: *.mat MATLAB data file with a MATLAB structure. *.xml file with a structure