Research Group of Prof. Dr. M. Griebel
Institute for Numerical Simulation

  author = {G. W. Zumbusch},
  title = {Symmetric Hierarchical Polynomials for the h-p-Version of
		  Finite Elements},
  institution = {Konrad-Zuse-Zentrum},
  address = {Berlin, Germany},
  year = {1993},
  number = {SC-93-32},
  ps = { 1},
  pdf = { 1},
  annote = {unrefereed},
  abstract = {Adaptive numerical methods using the $h$-$p$-version 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 well-suited
		  for the $p$- and $h$-$p$-version 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.}