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

  author = {G. W. Zumbusch},
  title = {Adaptive h-p approximation procedures, graded meshes and
		  anisotropic refinement for Numerical Quadrature},
  booktitle = {Proceedings of The First European Conference on Numerical
		  Mathematics and Advanced Applications, ENUMATH 95},
  editor = {F. Brezzi and J. Periaux and R. Glowinski and R. Rannacher
		  and Yu. Kuznetsov},
  year = {1995},
  note = {accepted, also as report SC-95-24 ZIB, Berlin},
  pages = {12},
  ps = { 1},
  pdf = { 1},
  annote = {refereed},
  abstract = {A set of adaptive algorithms for quadrature on
		  multi-dimensional polyhedral domains is presented. Several
		  kinds of refinement are discussed, covering local
		  improvement of quadrature order and splitting the domain
		  into sub-domains, resulting in isotropic, graded or
		  anisotropic grids. The algorithms are pure local heuristics
		  using no a priori knowledge or tuning parameters. This
		  approach was motivated by results from finite element
		  theory for optimal approximation results. Numerical
		  experiments show the optimality of pure local greedy-like
		  algorithms for singularity-type functions typically
		  occurring in finite element computations.}