A mixed nonoverlapping covolume method on quadrilateral grids for elliptic problems

X. Zhao, Y. Chen, J. Lv

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    A covolume method is proposed for the mixed formulation of second-order elliptic problems. The solution domain is divided by a quadrilateral grid, corresponding to which a nonoverlapping dual grid is constructed. The velocity and pressure are approximated by the lowest-order Raviart–Thomas space on quadrilaterals. We prove its first order optimal rate of convergence for the approximate velocities in the H(div)-norm as well as for the approximate pressures in the L2-norm. A second order error estimate between a suitable projection of the exact velocity (or pressure) and the approximate velocity (or approximate pressure) is also presented. Numerical experiments are provided to illustrate the error behavior of the scheme. Keywords: Mixed covolume method; Nonoverlapping covolume; Quadrilateral grid; Error estimate; Superconvergence
    Original languageEnglish
    Pages (from-to)23-40
    JournalJournal of Computational and Applied Mathematics
    Publication statusPublished - 15 Jan 2016


    • Mixed covolume method
    • Nonoverlapping covolume
    • Quadrilateral grid
    • Error estimate
    • Superconvergence


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