| 非定常不可压Navier-Stokes方程两重网格方法的稳定性和L2误差估计 |
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| 引用本文： | 任春风,马逸尘.非定常不可压Navier-Stokes方程两重网格方法的稳定性和L2误差估计[J].系统科学与数学,2006,26(4):407-425. |
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| 作者姓名： | 任春风 马逸尘 |
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| 作者单位： | 西安交通大学理学院,西安,710049 |
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| 基金项目： | 国家自然科学基金资助课题(10371096) |
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| 摘 要： | 讨论了二维非定常不可压Navier-Stokes方程的两重网格方法．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Stokes问题．采用一种新的全离散(时间离散用Crank-Nicolson格式,空间离散用混合有限元方法)格式数值求解N-S方程．证明了该全离散格式的稳定性．给出了L2误差估计．对比标准有限元方法,在保持同样精度的前提下,TGM能节省大量的计算量．
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| 关 键 词： | 非定常Navier-Stokes方程 两重网格方法 Crank-Nicolson格式 稳定性 |
| 修稿时间： | 2004年12月14 |
Error Estimate and Stability of a Two-grid Method for the Unsteady Incompressible Navier-Stokes Equations |
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| Ren Chunfeng,Ma Yichen.Error Estimate and Stability of a Two-grid Method for the Unsteady Incompressible Navier-Stokes Equations[J].Journal of Systems Science and Mathematical Sciences,2006,26(4):407-425. |
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| Authors: | Ren Chunfeng Ma Yichen |
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| Institution: | College of Science, Xi'an Jiaotong University, Xi'an 710049 |
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| Abstract: | A two-grid method for the unsteady Navier-Stokes equations modelling viscous incompressible flow is discussed in R2, which consists of finding a solution for a nonlinear problem on a coarse grid and a solution for the Stokes problem on a fine grid. A new fully discrete scheme for the numerical solution of these equations is also considered where the spatial discreteness is the mixed finite elements and the temporal discreteness is the Crank-Nicolson scheme. The stability for this scheme is proved and an L2 error estimate is also given. Compared with the usual finite element method, this method can save a lot of computation time under the same convergence accuracy. |
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| Keywords: | Unsteady Navier-Stokes equations two-grid method Crank-Nicolson scheme stability |
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