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Weng, Zhifeng; Cai, Yaoxiong

An efficient algorithm with stabilized finite element method for the Stokes eigenvalue problem. (English) Zbl 1426.76317

Math. Probl. Eng. 2017, Article ID 6362505, 9 p. (2017).
Summary: This paper provides a two-space stabilized mixed finite element scheme for the Stokes eigenvalue problem based on local Gauss integration. The two-space strategy contains solving one Stokes eigenvalue problem using the \(P_1 - P_1\) finite element pair and then solving an additional Stokes problem using the \(P_2 - P_2\) finite element pair. The postprocessing technique which increases the order of mixed finite element space by using the same mesh can accelerate the convergence rate of the eigenpair approximations. Moreover, our method can save a large amount of computational time and the corresponding convergence analysis is given. Finally, numerical results are presented to confirm the theoretical analysis.

Cited in 2 Documents

MSC:

76M10 Finite element methods applied to problems in fluid mechanics
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N25 Numerical methods for eigenvalue problems for boundary value problems involving PDEs
76D07 Stokes and related (Oseen, etc.) flows
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References:

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