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Superconvergence of mixed covolume method on quadrilateral grids for elliptic problems

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Abstract

This paper considers the mixed covolume method for the second-order elliptic equations over quadrilaterals. Superconvergence results are established in this paper on quadrilateral grids satisfying the h 2-parallelogram condition when the lowest-order Raviart-Thomas space is employed in the mixed covolume method. The authors prove O(h 2) accuracy between the approximate velocity or pressure and a suitable projection of the real velocity or pressure in the L 2 norm. Numerical experiments illustrating the theoretical results are provided.

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Authors and Affiliations

  1. Institute of Mathematics, Jilin University, Changchun, 130012, China

    Wanfu Tian

  2. School of Mathematics, Jilin University, Changchun, 130012, China

    Yonghai Li

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  1. Wanfu Tian
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  2. Yonghai Li
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Correspondence to Yonghai Li.

Additional information

This research is supported by the ‘985’ program of Jilin University, the National Natural Science Foundation of China under Grant No. 10971082, and the NSAF of China under Grant No. 11076014.

This paper was recommended for publication by Editor Ningning YAN.

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Tian, W., Li, Y. Superconvergence of mixed covolume method on quadrilateral grids for elliptic problems. J Syst Sci Complex 25, 385–397 (2012). https://doi.org/10.1007/s11424-011-9208-8

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  • DOI: https://doi.org/10.1007/s11424-011-9208-8

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