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Mathematical Problems in Engineering
Volume 2017, Article ID 6362505, 9 pages
https://doi.org/10.1155/2017/6362505
Research Article

An Efficient Algorithm with Stabilized Finite Element Method for the Stokes Eigenvalue Problem

School of Mathematics Science, Huaqiao University, Quanzhou 362021, China

Correspondence should be addressed to Zhifeng Weng; moc.361@htamwfz

Received 5 September 2017; Revised 12 November 2017; Accepted 23 November 2017; Published 31 December 2017

Academic Editor: Vassilios C. Loukopoulos

Copyright © 2017 Zhifeng Weng and Yaoxiong Cai. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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 finite element pair and then solving an additional Stokes problem using the 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.