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A two-grid block-centered finite difference method for nonlinear non-Fickian flow model

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  • Li, Xiaoli
  • Rui, Hongxing

Abstract

In this paper, a two-grid block-centered finite difference scheme is introduced and analyzed to solve the nonlinear parabolic integro-differential equation arising in modeling non-Fickian flow in porous media. This method is considered where the nonlinear problem is solved only on a coarse grid of size H and a linear problem is solved on a fine grid of size h. Error estimates are established on non-uniform rectangular grid which show that the discrete L∞(L2) and L2(H1) errors are O(▵t+h2+H3). Finally, some numerical experiments are presented to show the efficiency of the two-grid method and verify that the convergence rates are in agreement with the theoretical analysis.

Suggested Citation

  • Li, Xiaoli & Rui, Hongxing, 2016. "A two-grid block-centered finite difference method for nonlinear non-Fickian flow model," Applied Mathematics and Computation, Elsevier, vol. 281(C), pages 300-313.
    • Handle: RePEc:eee:apmaco:v:281:y:2016:i:c:p:300-313
    DOI: 10.1016/j.amc.2016.01.056
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    Cited by:

    1. Li, Xiaoli & Rui, Hongxing, 2017. "Characteristic block-centered finite difference method for compressible miscible displacement in porous media," Applied Mathematics and Computation, Elsevier, vol. 314(C), pages 391-407.
    2. Dossan Baigereyev & Dinara Omariyeva & Nurlan Temirbekov & Yerlan Yergaliyev & Kulzhamila Boranbek, 2022. "Numerical Method for a Filtration Model Involving a Nonlinear Partial Integro-Differential Equation," Mathematics, MDPI, vol. 10(8), pages 1-24, April.

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