HUANG Peng-zhan, HE Yin-nian, FENG Xin-long. A Two-Level Stabilized Finite Element Method for the Stokes Eigenvalue Problem[J]. Applied Mathematics and Mechanics, 2012, 33(5): 588-597. doi: 10.3879/j.issn.1000-0887.2012.05.007
Citation: HUANG Peng-zhan, HE Yin-nian, FENG Xin-long. A Two-Level Stabilized Finite Element Method for the Stokes Eigenvalue Problem[J]. Applied Mathematics and Mechanics, 2012, 33(5): 588-597. doi: 10.3879/j.issn.1000-0887.2012.05.007

A Two-Level Stabilized Finite Element Method for the Stokes Eigenvalue Problem

doi: 10.3879/j.issn.1000-0887.2012.05.007
  • Received Date: 2011-05-04
  • Rev Recd Date: 2012-02-10
  • Publish Date: 2012-05-15
  • A two-level stabilized finite element method for the Stokes eigenvalue problem based on local Gauss integration was considered. The method involved solving a Stokes eigenvalue problem on a coarse mesh with mesh size H and a Stokes problem on a fine mesh with mesh size h=O(H2), which can still maintain an asymptotically optimal accuracy. The given method provided an approximate solution with the convergence rate of the same order as the usual stabilized finite element solution, which involved solving a Stokes eigenvalue problem on a fine mesh with mesh size h.Hence, the method can save a large amount of computational time. Moreover, numerical tests confirmed the theoretical results of the presented method.
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