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 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. Key words. meshless methods, gridless discretizations, particle methods, Galerkin methods, partition of unity methods, Lagrange multipliers, h-version, p-version, advection, convection-diffusion AMS subject classifications. 65M60, 65M25, 65C05, ..