Affiliations: [a] School of Economics and Management, Beijing Jiaotong University, Beijing, P. R. China | [b]
Institute of Applied Physics and Computational Mathematics, Beijing, P. R. China
Correspondence:
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Corresponding author. Shuhong Song, Institute of Applied Physics and Computational Mathematics, No. 2, Fenghao Donglu, Haidian District (100094), Beijing, P.R. China. E-mail: song_shuhong@iapcm.ac.cn.
Abstract: Most of numerical methods for diffusion equations, refer to vertex unknowns directly or indirectly, and their accuracy is ultimately determined by the approximation to vertex unknowns. Based on the “twin-fitting” method, a simple and high accurate treatment for the vertex unknowns is developed and is applied to the nine-point scheme for diffusion problem. Numerical experiments show that the resulting nine-point scheme is high accurate for diffusion problems with discontinuous diffusion coefficients on distorted meshes.
Keywords: Discontinuous diffusion
coefficients, distorted meshes, the “twin-fitting”
method, the treatment for the vertex unknowns
