M. Griebel and M. A. Schweitzer.
A particle-partition of unity method for the solution of elliptic,
parabolic and hyperbolic PDE.
SIAM J. Sci. Comp., 22(3):853-890, 2000.
also as SFB Preprint 600, SFB 256, Institut für Angewandte
Mathematik, Universität Bonn.
[ bib | .ps.gz 1 ]
In this paper, we present a meshless discretization technique for instationary convection-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.