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

Author

Listed:
  • Peng, Jie
  • Shu, Shi
  • Yu, HaiYuan
  • Feng, Chunsheng
  • Kan, Mingxian
  • Wang, Ganghua

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.

Suggested Citation

  • Peng, Jie & Shu, Shi & Yu, HaiYuan & Feng, Chunsheng & Kan, Mingxian & Wang, Ganghua, 2017. "Error estimates on a finite volume method for diffusion problems with interface on rectangular grids," Applied Mathematics and Computation, Elsevier, vol. 311(C), pages 335-352.
    • Handle: RePEc:eee:apmaco:v:311:y:2017:i:c:p:335-352
    DOI: 10.1016/j.amc.2017.05.029
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    References listed on IDEAS

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    1. Wang, Tongke & Zhang, Zhiyue, 2015. "A compact finite volume method and its extrapolation for elliptic equations with third boundary conditions," Applied Mathematics and Computation, Elsevier, vol. 264(C), pages 258-271.
    2. Ewing, Richard E. & Li, Zhilin & Lin, Tao & Lin, Yanping, 1999. "The immersed finite volume element methods for the elliptic interface problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 50(1), pages 63-76.
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