Acceleration of two-grid stabilized mixed finite element method for the Stokes eigenvalue problem

Xinlong Feng; Zhifeng Weng; Hehu Xie

Applications of Mathematics (2014)

  • Volume: 59, Issue: 6, page 615-630
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Feng, Xinlong, Weng, Zhifeng, and Xie, Hehu. "Acceleration of two-grid stabilized mixed finite element method for the Stokes eigenvalue problem." Applications of Mathematics 59.6 (2014): 615-630. <http://eudml.org/doc/262046>.

@article{Feng2014,
abstract = {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.},
author = {Feng, Xinlong, Weng, Zhifeng, Xie, Hehu},
journal = {Applications of Mathematics},
keywords = {accelerated two grid method; Stokes eigenvalue problem; stabilized method; equal-order pair; error estimate; accelerated two grid method; Stokes eigenvalue problem; stabilized method; equal-order pair; error estimate; algorithm; convergence; numerical experiments},
language = {eng},
number = {6},
pages = {615-630},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Acceleration of two-grid stabilized mixed finite element method for the Stokes eigenvalue problem},
url = {http://eudml.org/doc/262046},
volume = {59},
year = {2014},
}

TY - JOUR
AU - Feng, Xinlong
AU - Weng, Zhifeng
AU - Xie, Hehu
TI - Acceleration of two-grid stabilized mixed finite element method for the Stokes eigenvalue problem
JO - Applications of Mathematics
PY - 2014
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 59
IS - 6
SP - 615
EP - 630
AB - 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.
LA - eng
KW - accelerated two grid method; Stokes eigenvalue problem; stabilized method; equal-order pair; error estimate; accelerated two grid method; Stokes eigenvalue problem; stabilized method; equal-order pair; error estimate; algorithm; convergence; numerical experiments
UR - http://eudml.org/doc/262046
ER -

References

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