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Student Number 942201021 Author Yun-Tsz Wang(王韻詞) Author's Email Address No Public. Statistics This thesis had been viewed 1346 times. Download 512 times. Department Mathematics Year 2007 Semester 2 Degree Master Type of Document Master's Thesis Language English Title On Two Iterative Least-Squares Finite Element Schemes for Solving the Incompressible Navier-Stokes Equations Date of Defense 2008-01-03 Page Count 25 Keyword driven cavity flows finite element methods iterative methods least squares Navier-Stokes equations Oseen equations Abstract This thesis is devoted to a numerical study of two iterative least-squares finite element schemes on uniform meshes for solving the stationary incompressible Navier-Stokes equations with velocity boundary condition. Introducing vorticity as an additional unknown variable, the Navier-Stokes problem can be recast as a first-order quasilinear velocity-vorticity-pressure system. Two Picard-type iterative least-squares finite element schemes are proposed for approximating the solution to the nonlinear first-order problem. In each iteration, we apply the usual L2 least-squares scheme or a weighted L2 least-squares scheme to solve the corresponding Oseen problem. We concentrate on two-dimensional model problems using continuous piecewise polynomial finite elements on uniform meshes for both iterative least-squares schemes. Numerical evidences show that, for the same test problem with smooth exact solution, the L2 least-squares solutions are more accurate than the weighted L2 least-squares solutions for low Reynolds number flows, while for flows with relatively higher Reynolds numbers the weighted L2 least-squares approximations seem to be better than the L2 least-squares approximations. Finally, numerical results for driven cavity flows are also given to demonstrate the effectiveness of the iterative least-squares finite element approach. Table of Content 中文摘要 ……………………………………………………………… i

英文摘要 …………………………………………………………… ii

目錄 ………………………………………………………………… iii

Abstract ……………………………………………………………… 1

1. Problem formulation …………………………………………… 2

2. Least-squares finite element schemes …………………… 6

3. Analysis of the least-squares finite element schemes for the Oseen problem …………………………………………… 10

4. Numerical experiments ……………………………………… 13

5. Numerical results of driven cavity flows ……………… 17

6. Conclusions …………………………………………………… 23

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Meth. Appl. Sci., 21 (1998), pp. 1637-1654.Advisor Suh-Yuh Yang(楊肅煜)

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942201021.pdf Date of Submission 2008-05-18

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