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The use of PDE centres in the local RBF Hermitian method for 3D convective-diffusion problems |
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| Authors: | David Stevens Henry PowerMichael Lees Herve Morvan |
| Institution: | School of Mechanical, Materials and Manufacturing Engineering, University of Nottingham, University Park, Nottingham, Nottinghamshire NG7 2RD, UK |
| Abstract: | In this work an extension is proposed to the Local Hermitian Interpolation (LHI) method; a meshless numerical method based on interpolation with small and heavily overlapping radial basis function (RBF) systems. This extension to the LHI method uses interpolation functions which themselves satisfy the partial differential equation (PDE) to be solved. In this way, a much improved reconstruction of partial derivatives can be obtained, resulting in significantly improved accuracy in many cases. |
| Keywords: | Numerical solution Initial and boundary value problems Meshless collocation approach Radial basis function Local collocation Implicit time stepping scheme |
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