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Unconditional convergence and superconvergence analysis for the transient Stokes equations with damping

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  • Li, Zhenzhen
  • Li, Minghao
  • Shi, Dongyang

Abstract

In this paper, the linearized backward Euler scheme for the transient Stokes equations with damping is presented, in which the velocity and pressure are approximated by the lowest-order Bernadi-Raugel rectangular element pair. Unconditional optimal error estimates of the velocity in the norms L∞(L2) and L∞(H1), and the pressure in the norm L∞(L2) are derived through the Stokes operator and the H−1-norm estimate. Moreover, the superclose properties and global superconvergent results are obtained by the interpolation post-processing technique. Finally, some numerical results are provided to confirm the theoretical analysis.

Suggested Citation

  • Li, Zhenzhen & Li, Minghao & Shi, Dongyang, 2021. "Unconditional convergence and superconvergence analysis for the transient Stokes equations with damping," Applied Mathematics and Computation, Elsevier, vol. 389(C).
    • Handle: RePEc:eee:apmaco:v:389:y:2021:i:c:s0096300320305282
    DOI: 10.1016/j.amc.2020.125572
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    References listed on IDEAS

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    1. Shi, Dongyang & Wang, Junjun, 2017. "Unconditional superconvergence analysis of conforming finite element for nonlinear parabolic equation," Applied Mathematics and Computation, Elsevier, vol. 294(C), pages 216-226.
    2. Shi, Dongyang & Yang, Huaijun, 2017. "Unconditional optimal error estimates of a two-grid method for semilinear parabolic equation," Applied Mathematics and Computation, Elsevier, vol. 310(C), pages 40-47.
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