Left: nodal linear basis functions spanning a nine-dimensional finite element space. Right: hierarchical linear basis functions spanning the same nine-dimensional finite element space; top to bottom: the 2 level 0 functions, the single level 1 function, the 2 level 2 functions, and the 4 level 3 function.

Left: quadratic hierarchical basis functions spanning a 17-dimensional, quadratic finite element space. Right: An alternate set of quadratic hierarchical basis functions spanning the same 17-dimensional, quadratic finite element space.