A PARTICLE-PARTITION OF UNITY METHOD FOR THE SOLUTION OF ELLIPTIC, PARABOLIC, AND HYPERBOLIC PDES.

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-version or a 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. [ABSTRACT FROM AUTHOR]