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

  author = {M. Griebel and M.~A. Schweitzer},
  title = {A Particle-Partition of Unity Method for the Solution of
		  Elliptic, Parabolic and Hyperbolic {PDE}},
  journal = {SIAM J. Sci. Comp.},
  year = {2000},
  optkey = {},
  volume = {22},
  number = {3},
  pages = {853--890},
  optmonth = {},
  ps = { 1},
  abstract = {In this paper, we present a meshless discretization
		  technique for instationary convec\-tion-diffusion problems.
		  It is based on operator splitting, the method of
		  characteristics and a generalized partition of unity
		  method. We focus on the discretization process and its
		  quality. The method may be used as an h- or p-version. Even
		  for general particle distributions, the convergence
		  behavior of the different versions corresponds to that of
		  the respective version of the finite element method on a
		  uniform grid. We discuss the implementational aspects of
		  the proposed method. Furthermore, we present the results of
		  numerical examples, where we considered instationary
		  convection-diffusion, instationary diffusion, linear
		  advection and elliptic problems.},
  note = {also as SFB Preprint 600, SFB 256, Institut f\"ur
		  Angewandte Mathematik, Universit\"at Bonn},
  annote = {refereed article,256D}