Adaptive meshless centres and RBF stencils for Poisson equation

Oleg Davydov; Dang Thi Oanh

doi:10.1016/j.jcp.2010.09.005

Adaptive meshless centres and RBF stencils for Poisson equation

Oleg Davydov, Dang Thi Oanh

Mathematics And Statistics

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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.

Original language	English
Pages (from-to)	287-304
Number of pages	18
Journal	Journal of Computational Physics
Volume	230
Issue number	2
DOIs	https://doi.org/10.1016/j.jcp.2010.09.005
Publication status	Published - 20 Jan 2011

Keywords

adaptive methods
meshless methods
radial basis functions
poisson equation

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10.1016/j.jcp.2010.09.005

Rbf poissonSubmitted manuscript, 387 KB

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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.",

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AU - Oanh, Dang Thi

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AB - 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.

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KW - meshless methods

KW - radial basis functions

KW - poisson equation

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ER -

Adaptive meshless centres and RBF stencils for Poisson equation

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Keywords

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