Journal
SIAM JOURNAL ON SCIENTIFIC COMPUTING
Volume 22, Issue 3, Pages 853-890Publisher
SIAM PUBLICATIONS
DOI: 10.1137/S1064827599355840
Keywords
meshless methods; gridless discretizations; particle methods; Galerkin methods; partition of unity methods; Lagrange multipliers; h-version; p-version; advection; convection-diffusion
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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-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.
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