Error estimates on a finite volume method for diffusion problems with interface on Eulerian grids
Abstract
The finite volume methods are frequently employed in the discretization of diffusion problems with interface. In this paper, we firstly present a vertex-centered MACH-like finite volume method for solving stationary diffusion problems with strong discontinuity and multiple material cells on the Eulerian grids. This method is motivated by Frese [No. AMRC-R-874, Mission Research Corp., Albuquerque, NM, 1987]. Then, the local truncation error and global error estimates of the degenerate five-point MACH-like scheme are derived by introducing some new techniques. Especially under some assumptions, we prove that this scheme can reach the asymptotic optimal error estimate in the maximum norm. Finally, numerical experiments verify theoretical results.
Keywords
Cite
@article{arxiv.1609.00827,
title = {Error estimates on a finite volume method for diffusion problems with interface on Eulerian grids},
author = {Jie Peng and Shi Shu and Haiyuan Yu and Chunsheng Feng and Mingxian Kan and Ganghua Wang},
journal= {arXiv preprint arXiv:1609.00827},
year = {2016}
}