Navier-Stokes方程流函数形式两重网格算法的误差分析

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基金项目: 国家自然科学基金资助(10001028)

Two-Grid Error Estimates for the Stream Function Form of Navier-Stokes Equations

摘要: 对定常Navier-Stokes方程流函数形式两重网格有限元算法进行了误差分析。此方法包括在粗网格上求解一个非线性问题,在细网格上求解一个线性问题,然后再在粗网格上求解一个线性校正问题。分析了包括校正项和不包括校正项两种方法的误差,得出对于任意固定的Reynolds数,能达到最优逼近阶。
- Navier-Stokes方程 /
- 两重网格方法 /
- 流函数
Abstract: The two-grid finite element approximation to the stream function form of the stationary Navier-Stokes equations was analyzed. The algorithms involve solving one small, nonlinear coarse mesh system, one linear problem on the fine mesh system, and a linear correct problem on the coarse mesh. The algorithms with the correct problem and without the correct problem were discussed. The algorithms produce an approximate solution with the optimal, asymptotic accuracy for any fixed Reynolds number.
- Navier-Stokes equation /
- two-grid method /
- stream function

[1]	Layton W,Ye X.Two level discretizations of the stream function form of the Navier-Stokes equations[J].J Numer Functions Anal,1999,20(9/10):909-916.
[2]	Ye X.Two-grid discretizations with backtracking of the stream function form of the Navier-Stokes equations[J].Appl Math Comput,1999,100(2/3):131-138.
[3]	Girault V,Raviart P A.Finite Element Methods for the Navier-Stokes Equations:Theory and Algorithms[M].Berlin:Springer,1986.
[4]	Girault V,Raviart P A.Finite Element Methods for the Navier-Stokes equations[M].Vol 749 Berlin:Springer LNM,1979.
[5]	Xu J.Two-grid discretization techniques for linear and nonlinear PDEs[J].SIAM J Numer Anual,1996,33(5):1759-1777

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