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

作者：Yuan Guangwei; Sheng Zhiqiang^*

来源：Journal of Computational Physics, 2007, 224(2): 1170-1189.

DOI：10.1016/j.jcp.2006.11.011

• diffusion equations
• finite volume scheme
• distorted mesh
• accuracy

We investigate the convergence of a finite volume scheme for the approximation of diffusion operators on distorted meshes. The method was originally introduced by Hermetine [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.

• 出版日期2007-6-10
• 单位北京应用物理与计算数学研究所