Geodesic
Acceleration of two-grid stabilized mixed finite element method for the Stokes eigenvalue problem
Applications of Mathematics, Tome 59 (2014) no. 6, pp. 615-630.

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This paper provides an accelerated two-grid stabilized mixed finite element scheme for the Stokes eigenvalue problem based on the pressure projection. With the scheme, the solution of the Stokes eigenvalue problem on a fine grid is reduced to the solution of the Stokes eigenvalue problem on a much coarser grid and the solution of a linear algebraic system on the fine grid. By solving a slightly different linear problem on the fine grid, the new algorithm significantly improves the theoretical error estimate which allows a much coarser mesh to achieve the same asymptotic convergence rate. Finally, numerical experiments are shown to verify the high efficiency and the theoretical results of the new method.
DOI : 10.1007/s10492-014-0076-0
Classification : 65N12, 65N25, 65N30, 76D07
Keywords: accelerated two grid method; Stokes eigenvalue problem; stabilized method; equal-order pair; error estimate 
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     title = {Acceleration of two-grid stabilized mixed finite element method for the {Stokes} eigenvalue problem},
     journal = {Applications of Mathematics},
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     publisher = {mathdoc},
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     url = {http://geodesic.mathdoc.fr/articles/10.1007/s10492-014-0076-0/}
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Feng, Xinlong; Weng, Zhifeng; Xie, Hehu. Acceleration of two-grid stabilized mixed finite element method for the Stokes eigenvalue problem. Applications of Mathematics, Tome 59 (2014) no. 6, pp. 615-630. doi : 10.1007/s10492-014-0076-0. http://geodesic.mathdoc.fr/articles/10.1007/s10492-014-0076-0/

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