Adaptive Wavelet Solution to the Stokes Problem  

作　　者：Ying-chun Jiang Youming Liu 

机构地区：[1]College of Mathematics and Computer Sciences, Guilin University of Electronic Technology, Cuilin 541004, China [2]Department of Applied Mathematics, Beijing University of Technology, Beijing 100022, China

出　　处：《Acta Mathematicae Applicatae Sinica》2008年第4期613-626,共14页应用数学学报（英文版）

基　　金：Supported by the Natural Science Foundation of Beijing(No.1082003).

摘　　要：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 M0 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.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 M0 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.

关 键 词：Richardson iteration adaptive algorithm WAVELETS Stokes problem Galerkin solution 

分 类 号：O411.1[理学—理论物理]