Adaptive meshless centres and RBF stencils for Poisson equation

Authors:
Oleg Davydov;Dang Thi Oanh
Affiliations:
Department of Mathematics and Statistics, University of Strathclyde, 26 Richmond Street, Glasgow G1 1XH, Scotland, UK;Department of Computer Science, Faculty of Information Technology, Thai Nguyen University, Quyet Thang Commune, Thai Nguyen City, Viet Nam
Venue:
Journal of Computational Physics
Year:
2011

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Abstract

We consider adaptive meshless discretisation of the Dirichlet problem for Poisson equation based on numerical differentiation stencils obtained with the help of radial basis functions. New meshless stencil selection and adaptive refinement algorithms are proposed in 2D. Numerical experiments show that the accuracy of the solution is comparable with, and often better than that achieved by the mesh-based adaptive finite element method.