压力边界条件下的Stokes问题的混合有限元分析  

A mixed finite element method for the Stokes problem with pressure boundary condition

作　　者：段火元 吴先亮 DUAN Huo-yuan;WU Xian-liang(School of Mathematics and Statistics,Wuhan University,Wuhan 430072,China)

机构地区：[1]武汉大学数学与统计学院,湖北武汉430072

出　　处：《高校应用数学学报（A辑）》2022年第2期177-186,共10页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：国家自然科学基金(11971366)。

摘　　要：研究了用于数值求解一类非标准条件(压力Dirichlet边界条件)下具有非H^(1)空间速度解的Stokes问题的Taylor-Hood单元混合有限元方法.文中证明了这些单元对于非H^(1)空间速度解是正确收敛的.理论分析中采用了最大inf-sup条件和Hahn-Banach延拓的新技巧.也给出了数值计算结果用于验证收敛性.A mixed finite element method with Taylor-Hood elements for solving the non H^(1) velocity solution of the Stokes problem with pressure Dirichlet boundary conditions is studied.And it is proved that these elements are correctly convergent for the singular velocity solution because of the non-smooth domain.The new techniques in the theoretical analysis are the maximal inf-sup condition and the Hahn-Banach extension.Numerical results are also given to verify the convergence.

关 键 词：STOKES问题 混合有限元方法 Taylor-Hood单元 最大inf-sup条件 Hahn-Banach延拓 

分 类 号：O241.82[理学—计算数学]