Research Group of Prof. Dr. J. Schweitzer
Institute for Numerical Simulation

  author = {M. Griebel and M.~A. Schweitzer},
  title = {{A} {P}article-{P}artition of {U}nity {M}ethod for the
		  Solution of {E}lliptic, {P}arabolic and {H}yperbolic
  journal = {SIAM J. Sci. Comput.},
  year = {2000},
  volume = {22},
  pages = {853--890},
  number = {3},
  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.},
  annote = {refereed article,256D,ag-schweitzer},
  optnote = {also as SFB Preprint 600, SFB 256, Institut f\"ur
		  Angewandte Mathematik, Universit\"at Bonn},
  ps = { 1}