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Analysis of accuracy of a finite volume scheme for diffusion equations on distorted meshes

✍ Scribed by Guangwei Yuan; Zhiqiang Sheng

Publisher: Elsevier Science
Year: 2007
Tongue: English
Weight: 333 KB
Volume: 224
Category: Article
ISSN: 0021-9991
DOI: 10.1016/j.jcp.2006.11.011

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✦ Synopsis

We investigate the convergence of a finite volume scheme for the approximation of diffusion operators on distorted meshes. The method was originally introduced by Hermeline [F. Hermeline, A finite volume method for the approximation of diffusion operators on distorted meshes, J. Comput. Phys. 160 (2000) 481-499], which has the advantage that highly distorted meshes can be used without the numerical results being altered. In this work, we prove that this method is of first-order accuracy on highly distorted meshes. The results are further extended to the diffusion problems with discontinuous coefficient and non-stationary diffusion problems. Numerical experiments are carried out to confirm the theoretical predications.

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