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 引用本文: 刘庆芳, 侯延仁. 非定常对流扩散方程的局部和并行有限元算法[J]. 应用数学和力学, 2009, 30(6): 733-740.
LIU Qing-fang, HOU Yan-ren. Local and Parallel Finite Element Algorithms for the Time-Dependent Convection-Diffusion Equations[J]. Applied Mathematics and Mechanics, 2009, 30(6): 733-740. doi: 10.3879/j.issn.1000-0887.2009.06.013
 Citation: LIU Qing-fang, HOU Yan-ren. Local and Parallel Finite Element Algorithms for the Time-Dependent Convection-Diffusion Equations[J]. Applied Mathematics and Mechanics, 2009, 30(6): 733-740.

## 非定常对流扩散方程的局部和并行有限元算法

##### doi: 10.3879/j.issn.1000-0887.2009.06.013

###### 作者简介:刘庆芳(1982- ),女,济南人,博士(联系人.E-mail:qfliu08@hotmail.com).
• 中图分类号: O241.82

## Local and Parallel Finite Element Algorithms for the Time-Dependent Convection-Diffusion Equations

• 摘要: 对基于两重网格的非定常对流扩散方程的局部和并行有限元算法进行了研究．算法的理论依据是两重网格的思想，解的低频分量可以用一个整体的粗网格空间来逼近，高频分量可以用局部和并行的细网格空间来逼近．因此，这种局部和并行算法仅仅涉及一个粗网格上的整体逼近和细网格上的局部校正．得到了算法的误差估计，一些数值例子验证了算法的有效性．
•  [1] Xu J C,Zhou A H.Local and parallel finite element algorithms based on two-grid discretizations[J].Math Comput,1999,69(231):881-909. [2] Xu J C,Zhou A H.Local and parallel finite element algorithms based on two-grid discretizations for nonlinear problems[J].Adv Comput Math,2001,14(4):293-327. [3] Xu J C,Zhou A H.Some local and parallel properties of finite element discretizations[A].In:Lai C H,Bjφsted P E,Cross M,et al,Eds.Proceedings of the 11th International Conference on Domain Decomposition Methods[C],Greenwich:England,1999,140-147. [4] He Y N, Xu J C,Zhou A H.Local and parallel finite element algorithms for the Stokes problem[J].Numer Math,2008,109(3):415-434. [5] He Y N, Xu J C,Zhou A H.Local and parallel finite element algorithms for the Navier-Stokes problem[J].J Comput Math,2006,24(3):227-238. [6] 马飞遥,马逸尘,沃维丰.基于二重网络的定常Navier-Stokes方程的局部和并行有限元算法[J].应用数学和力学,2007,28(1):25-33. [7] Xu J C.A novel two-grid method for semilinear equations[J].SIAM J Sci Comput,1994,15(1):231-237. doi: 10.1137/0915016 [8] Xu J C. Two-grid discretization techniques for linear and nonlinear PDEs[J].SIAM J Numer Anal,1996,33(5):1759-1777. [9] Heywood J G,Rannacher R.Finite element approximation of the nonstationary Navier-Stokes problem,Part IV: Error analysis for second-order time discretization[J].SIAM J Numer Anal,1990,27(2):353-384. doi: 10.1137/0727022

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##### 出版历程
• 收稿日期:  2008-11-16
• 修回日期:  2009-05-06
• 刊出日期:  2009-06-15

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