对流占优扩散问题的经济型流线扩散有限元法  

ECONOMICAL FINITE DIFFERENCE-STREAMLINE DIFFUSION METHOD FOR CONVECTION-DOMINATED DIFFUSION PROBLEMS

作　　者：孙澈[1] 曹松[2] 

机构地区：[1]南开大学,天津300071 [2]铁道科学研究院电子所,北京100081

出　　处：《计算数学》2004年第3期367-384,共18页Mathematica Numerica Sinica

摘　　要：In this paper, the economical finite difference-streamline diffusion (EFDSD) schemes based on the linear F.E. space for time-dependent linear and non-linear convection-dominated diffusion problems are constructed. The stability and error estimation with quasi-optimal order approximation are established in the norm stronger than L^2 - norm for the schemes considered. It is indicated by the results obtained that,for linear F.E. space, the EFDSD schemes have the same specific properties of stability and convergence as the traditional FDSD schemes for the problems discussed.In this paper, the economical finite difference-streamline diffusion (EFDSD) schemes based on the linear F.E. space for time-dependent linear and non-linear convection-dominated diffusion problems are constructed. The stability and error estimation with quasi-optimal order approximation are established in the norm stronger than L2 - norm for the schemes considered. It is indicated by the results obtained that,for linear F.E. space, the EFDSD schemes have the same specific properties of stability and convergence as the traditional FDSD schemes for the problems discussed.

关 键 词：对流占优扩散问题 有限元算法 流线扩散法 FDSD方法 检验函数 稳定性 误差估计 

分 类 号：O241.82[理学—计算数学]