Error estimates on a finite volume method for diffusion problems with interface on rectangular grids

Jie Peng, Shi Shu, HaiYuan Yu, Chunsheng Feng, Mingxian Kan and Ganghua Wang

Applied Mathematics and Computation, 2017, vol. 311, issue C, 335-352

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|ln h|) in the maximum norm. Finally, numerical experiments verify theoretical results.

Keywords: Diffusion problems with interface; Finite volume method; Eulerian grids; Error estimates (search for similar items in EconPapers)
Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:311:y:2017:i:c:p:335-352

DOI: 10.1016/j.amc.2017.05.029

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