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

Lingling Sun and Yidu Yang

Applied Mathematics and Computation, 2022, vol. 421, issue C

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.

Keywords: Stokes eigenvalue problem; Nonconforming mixed finite element; A posteriori error estimates; Adaptive algorithms (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:421:y:2022:i:c:s0096300322000376

DOI: 10.1016/j.amc.2022.126951

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