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Error estimates on a finite volume method for diffusion problems with interface on rectangular grids
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DOI：10.1016/j.amc.2017.05.029.png)
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Abstract
En 中文
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(h(2)vertical bar In h vertical bar) in the maximum norm. Finally, numerical experiments verify theoretical results. (C) 2017 Elsevier Inc. All rights reserved.
Keywords:
Diffusion problems with interface
Finite volume method
Eulerian grids
Error estimates
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