3维Stokes问题的一种非协调-协调有限元法  

Nonconforming-conforming finite element method for 3D Stokes problem

作　　者：张敏[1] 罗鲲[1] 张世全[1] 

机构地区：[1]四川大学数学学院,成都610064

出　　处：《四川大学学报（自然科学版）》2018年第1期37-41,共5页Journal of Sichuan University(Natural Science Edition)

基　　金：国家自然科学基金(11401407)

摘　　要：本文提出了3维Stokes问题的一种非协调-协调有限元方法.在平行六面体网格下,本文使用速度-压力模型,速度的前两个分量使用非协调旋转Q_1元离散,第三个分量使用协调线性元离散,压力用分片常数.本文证明该有限元是稳定的,满足离散inf-sup条件且速度u的H^1半范和压力p的L^2范具有最优一阶收敛.数值试验验证了理论结果.Nonconforming finite element method for 3D Stokes problem is considered. Velocity-pressure model with parallelepipeds mesh is adopted. In this finite element, the nonconforming rotated Q1 ele- ments are used for the approximation of first two components of the velocity, the conforming linear ele- ment is used for the approximation of the third component, and the piecewise constant is used for the ap- proximation of pressure. Optimal error estimates are derived, which are both first order for H1 -semi- norm of velocity u and L2 norm of pressure p. Numerical experiments are provided to verify the theoreti- cal results.

关 键 词：STOKES问题 非协调旋转Q1元 INF-SUP条件 

分 类 号：O241.82[理学—计算数学]