@InProceedings{ Zumbusch:1995, 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 = {http://wissrech.ins.uni-bonn.de/research/pub/zumbusch/SC-95-24.ps.gz} , pdf = {http://wissrech.ins.uni-bonn.de/research/pub/zumbusch/SC-95-24.pdf} , 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.} }