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 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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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     author = {Feng, Xinlong and Weng, Zhifeng and Xie, Hehu},
     title = {Acceleration of two-grid stabilized mixed finite element method for the {Stokes} eigenvalue problem},
     journal = {Applications of Mathematics},
     pages = {615--630},
     year = {2014},
     volume = {59},
     number = {6},
     doi = {10.1007/s10492-014-0076-0},
     mrnumber = {3277730},
     zbl = {06391453},
     language = {en},
     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

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