[1] 
G. W. Zumbusch.
Symmetric hierarchical polynomials for the hpversion of finite
elements.
Technical Report SC9332, KonradZuseZentrum, Berlin, Germany,
1993. [ bib  .ps.gz 1  .pdf 1 ] Adaptive numerical methods using the hpversion of finite elements require special kinds of shape functions. Desirable properties of them are symmetry, hierarchy and simple coupling. In a first step it is demonstrated that for standard polynomial vector spaces not all of these features can be obtained simultaneously. However, this is possible if these spaces are extended. Thus a new class of polynomial shape functions is derived, which is wellsuited for the p and hpversion of finite elements on unstructured simplices. The construction is completed by minimizing the condition numbers of the arising finite element matrices. The new shape functions are compared with standard functions widely used in the literature.
