Hierarchic finite element bases on unstructured tetrahedral meshes

The problem of constructing hierarchic bases for nite element discretization of the spaces H1, H(curl), H(div) and L2 on tetrahedral elements is addressed. A simple and e cient approach to ensuring conformity of the approximations across element interfaces is described. Hierarchic bases of arbitrary polynomial order are presented. It is shown how these may be used to construct nite element approximations of arbitrary, non-uniform, local order approximation on unstructured meshes of curvilinear tetrahedral elements