Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5775742 | Applied Mathematics and Computation | 2017 | 18 Pages |
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 quadrilateral 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 O(h2|lnâh|) in the maximum norm. Finally, numerical experiments verify theoretical results.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Jie Peng, Shi Shu, HaiYuan Yu, Chunsheng Feng, Mingxian Kan, Ganghua Wang,