非定常线性化Navier-Stokes方程的非协调流线扩散有限元法分析  

Streamline Diffusion Nonconforming Finite Element Method for the Time-Dependent Linearized Navier-Stokes Equations

作　　者：陈豫眉[1,2] 谢小平[1] 

机构地区：[1]四川大学数学学院,成都610064 [2]西华师范大学数学与信息学院,四川南充637002

出　　处：《应用数学和力学》2010年第7期822-834,共13页Applied Mathematics and Mechanics

基　　金：国家自然科学基金资助项目(10771150);国家重点基础研究发展规划资助项目(2005CB321701);教育部新世纪优秀人才基金资助项目(NCET-07-0584);四川省教育厅青年基金资助项目(07ZB087)

摘　　要：对非定常线性化Navier-Stokes方程提出了非协调流线扩散有限元方法.用向后Euler格式离散时间,用流线扩散法处理扩散项带来的非稳定性.速度采用不连续的分片线性逼近,压力采用分片常数逼近.得到了离散解的存在唯一性以及在一定范数意义下离散解的稳定性和误差估计.A finite difference streamline diffusion nonconforming finite element approximation was proposed for solving the time-dependent linearized Navier-Stokes equations.Streamline diffusion finite element method was used to discretize the space variables in order to cope with the usual instabilities caused by the convection term and finite difference discretization was used in the time domain.Nonconforming finite element approximations were used for the velocity and pressure fields：the velocity is approximated by discontinuous piecewise linear and the pressure by piecewise constant.Stability and optimal error estimates for the discrete solutions are obtained.

关 键 词：流线扩散法 非协调 非定常线性化Navier-Stokes方程 误差估计 

分 类 号：O242.21[理学—计算数学]