Approximation of an eigenvalue problem associated with the Stokes problem by the stream function-vorticity-pressure method

Wei Chen; Qun Lin

Applications of Mathematics (2006)

  • Volume: 51, Issue: 1, page 73-88
  • ISSN: 0862-7940

Abstract

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By means of eigenvalue error expansion and integral expansion techniques, we propose and analyze the stream function-vorticity-pressure method for the eigenvalue problem associated with the Stokes equations on the unit square. We obtain an optimal order of convergence for eigenvalues and eigenfuctions. Furthermore, for the bilinear finite element space, we derive asymptotic expansions of the eigenvalue error, an efficient extrapolation and an a posteriori error estimate for the eigenvalue. Finally, numerical experiments are reported.

How to cite

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Chen, Wei, and Lin, Qun. "Approximation of an eigenvalue problem associated with the Stokes problem by the stream function-vorticity-pressure method." Applications of Mathematics 51.1 (2006): 73-88. <http://eudml.org/doc/33245>.

@article{Chen2006,
abstract = {By means of eigenvalue error expansion and integral expansion techniques, we propose and analyze the stream function-vorticity-pressure method for the eigenvalue problem associated with the Stokes equations on the unit square. We obtain an optimal order of convergence for eigenvalues and eigenfuctions. Furthermore, for the bilinear finite element space, we derive asymptotic expansions of the eigenvalue error, an efficient extrapolation and an a posteriori error estimate for the eigenvalue. Finally, numerical experiments are reported.},
author = {Chen, Wei, Lin, Qun},
journal = {Applications of Mathematics},
keywords = {eigenvalue problem; Stokes problem; stream function-vorticity-pressure method; asymptotic expansion; extrapolation; a posteriori error estimates; eigenvalue problem; Stokes problem; stream function-vorticity-pressure method; error expansion; convergence; eigenfunctions; bilinear finite element; extrapolation; error estimate; numerical experiments},
language = {eng},
number = {1},
pages = {73-88},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Approximation of an eigenvalue problem associated with the Stokes problem by the stream function-vorticity-pressure method},
url = {http://eudml.org/doc/33245},
volume = {51},
year = {2006},
}

TY - JOUR
AU - Chen, Wei
AU - Lin, Qun
TI - Approximation of an eigenvalue problem associated with the Stokes problem by the stream function-vorticity-pressure method
JO - Applications of Mathematics
PY - 2006
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 51
IS - 1
SP - 73
EP - 88
AB - By means of eigenvalue error expansion and integral expansion techniques, we propose and analyze the stream function-vorticity-pressure method for the eigenvalue problem associated with the Stokes equations on the unit square. We obtain an optimal order of convergence for eigenvalues and eigenfuctions. Furthermore, for the bilinear finite element space, we derive asymptotic expansions of the eigenvalue error, an efficient extrapolation and an a posteriori error estimate for the eigenvalue. Finally, numerical experiments are reported.
LA - eng
KW - eigenvalue problem; Stokes problem; stream function-vorticity-pressure method; asymptotic expansion; extrapolation; a posteriori error estimates; eigenvalue problem; Stokes problem; stream function-vorticity-pressure method; error expansion; convergence; eigenfunctions; bilinear finite element; extrapolation; error estimate; numerical experiments
UR - http://eudml.org/doc/33245
ER -

References

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