Overlapping domain decomposition method by radial basis functions
Applied Numerical Mathematics
A Generalized (Meshfree) Finite Difference Discretization for Elliptic Interface Problems
NMA '02 Revised Papers from the 5th International Conference on Numerical Methods and Applications
Multi-level partition of unity implicits
ACM SIGGRAPH 2003 Papers
A class of difference schemes with flexible local approximation
Journal of Computational Physics
Convergence of general meshless Schwarz method using radial basis functions
Applied Numerical Mathematics
Journal of Computational and Applied Mathematics
A meshless Galerkin method for Dirichlet problems using radial basis functions
Journal of Computational and Applied Mathematics
Domain decomposition by radial basis functions for time dependent partial differential equations
ACST'06 Proceedings of the 2nd IASTED international conference on Advances in computer science and technology
Multi-level partition of unity implicits
SIGGRAPH '05 ACM SIGGRAPH 2005 Courses
A note on the meshless method using radial basis functions
Computers & Mathematics with Applications
Journal of Computational and Applied Mathematics
Adjoint-based optimal control using meshfree discretizations
Journal of Computational and Applied Mathematics
Parallel generalized finite element method for magnetic multiparticle problems
VECPAR'04 Proceedings of the 6th international conference on High Performance Computing for Computational Science
Journal of Computational Physics
Parametric structural optimization with dynamic knot RBFs and partition of unity method
Structural and Multidisciplinary Optimization
Efficient analysis of transient heat transfer problems exhibiting sharp thermal gradients
Computational Mechanics
Quasi-optimal rates of convergence for the Generalized Finite Element Method in polygonal domains
Journal of Computational and Applied Mathematics
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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.