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Stability and convergence of characteristic MAC scheme and post-processing for the Oseen equations on non-uniform grids

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  • Li, Xiaoli
  • Rui, Hongxing

Abstract

In this paper, we establish the LBB condition and stability for both velocity and pressure of characteristic MAC scheme for the Oseen equations on non-uniform grids. We obtain the second order convergence in discrete L2 norm for both velocity and pressure and the first order convergence in discrete H1 norm for velocity. Moreover, we construct the post-processing characteristic MAC scheme to obtain second order accuracy in discrete H1 norm for the velocity. Finally, some numerical experiments are presented to show the correctness and accuracy of the MAC scheme.

Suggested Citation

  • Li, Xiaoli & Rui, Hongxing, 2019. "Stability and convergence of characteristic MAC scheme and post-processing for the Oseen equations on non-uniform grids," Applied Mathematics and Computation, Elsevier, vol. 342(C), pages 94-111.
    • Handle: RePEc:eee:apmaco:v:342:y:2019:i:c:p:94-111
    DOI: 10.1016/j.amc.2018.08.048
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    References listed on IDEAS

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    1. Bonaventura, Luca & Ferretti, Roberto & Rocchi, Lorenzo, 2018. "A fully semi-Lagrangian discretization for the 2D incompressible Navier–Stokes equations in the vorticity-streamfunction formulation," Applied Mathematics and Computation, Elsevier, vol. 323(C), pages 132-144.
    2. 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.
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