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The a posteriori error estimates and adaptive computation of nonconforming mixed finite elements for the Stokes eigenvalue problem

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  • Sun, Lingling
  • Yang, Yidu

Abstract

In this paper, we discuss the a posteriori error estimates and adaptive algorithm of non-conforming mixed finite elements including the Crouzeix–Raviart element and the enriched Crouzeix–Raviart element for the Stokes eigenvalue problem in Rd(d=2,3). We give the a posteriori error estimators and prove their reliability and efficiency. Based on the a posteriori error estimators we built two adaptive algorithms, the direct AFEM and the shifted-inverse AFEM. Numerical experiments and theoretical analysis are consistent, which indicates that the numerical eigenvalues obtained by the above two adaptive algorithms achieve the optimal convergence order O(dof−2d) and approximate the exact ones from below.

Suggested Citation

  • Sun, Lingling & Yang, Yidu, 2022. "The a posteriori error estimates and adaptive computation of nonconforming mixed finite elements for the Stokes eigenvalue problem," Applied Mathematics and Computation, Elsevier, vol. 421(C).
    • Handle: RePEc:eee:apmaco:v:421:y:2022:i:c:s0096300322000376
    DOI: 10.1016/j.amc.2022.126951
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    References listed on IDEAS

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    1. Yang Liu & Hong Li & Yanwei Du & Jinfeng Wang, 2013. "Explicit Multistep Mixed Finite Element Method for RLW Equation," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-12, May.
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