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Acta Mathematicae Applicatae Sinica 2008, Vol. 24 Issue (4) :613-626    DOI:
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Adaptive Wavelet Solution to the Stokes Problem
Ying-chun Jiang, Youming Liu
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Abstract This paper deals with the design and analysis of adaptive wavelet
method for the Stokes problem. First, the limitation of Richardson iteration
is explained and the multiplied matrix $M_0$ in the paper of Bramble and
Pasciak is proved to be the simplest possible in an appropiate sense. Similar
to the divergence operator, an exact application of its dual is shown; Second,
based on these above observations, an adaptive wavelet algorithm for the Stokes
problem is designed. Error analysis and computational complexity are given;
Finally, since our algorithm is mainly to deal with an elliptic and positive
definite operator equation, the last section is devoted to the Galerkin
solution of an elliptic and positive definite equation. It turns out that the
upper bound for error estimation may be improved.
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KeywordsRichardson iteration     
AbstractThis paper deals with the design and analysis of adaptive wavelet
method for the Stokes problem. First, the limitation of Richardson iteration
is explained and the multiplied matrix $M_0$ in the paper of Bramble and
Pasciak is proved to be the simplest possible in an appropiate sense. Similar
to the divergence operator, an exact application of its dual is shown; Second,
based on these above observations, an adaptive wavelet algorithm for the Stokes
problem is designed. Error analysis and computational complexity are given;
Finally, since our algorithm is mainly to deal with an elliptic and positive
definite operator equation, the last section is devoted to the Galerkin
solution of an elliptic and positive definite equation. It turns out that the
upper bound for error estimation may be improved.
KeywordsRichardson iteration     
Received: 1900-01-01;
Cite this article:   
.Adaptive Wavelet Solution to the Stokes Problem[J]  Acta Mathematicae Applicatae Sinica, 2008,V24(4): 613-626
URL:  
http://www.applmath.com.cn/jweb_yysxxb_en/EN/      或     http://www.applmath.com.cn/jweb_yysxxb_en/EN/Y2008/V24/I4/613
 
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