解Oseen方程的P_1非协调四边形单元的涡旋粘性法  

Stabilized Methods based on P_1-nonconforming Quadrilateral Finite Element for Oseen Equations

作　　者：左芳芳[1] 孔花[2] 刘程熙[2] 

机构地区：[1]四川大学数学学院,四川成都610064 [2]内江师范学院数学与信息科学学院,四川内江641112

出　　处：《四川师范大学学报（自然科学版）》2012年第5期632-638,共7页Journal of Sichuan Normal University（Natural Science）

基　　金：四川省科技攻关课题(05GG006-006-2)资助项目

摘　　要：解Oseen方程最主要的方法是混合有限元法,而这需要混合有限元空间满足离散的inf-sup(LBB)条件以及克服对流占优以防止数值解产生伪振荡.所采取的四边形网格上的P1-Q0元的非协调稳定化方法是通过L2局部投影添加涡旋粘性项来修正变分形式,增强其格式的稳定性,以绕开LBB条件,并克服对流占优.同时通过局部投影稳定化分析与最优误差估计,在理论上论证此方法的收敛性,使得P1非协调四边形元的应用更为广泛.The mixed finite element method is one of the main methods of solving Oseen equations, which requires the mixed finite element space to satisfy the discrete LBB condition and overcome the convection dominant phenomenon to avoid the numerical solution presenting fake oscillation. By adding a vortex viscidity term via L2 local projection, the nonconforming stabilization method for P^-Q0 finite element on quadrilateral grid used in this paper revises the variatioal form and enhances its stability to avoid the LBB condition and overcomes the convection dominant. By analtzing the stability of the local projection and estimating the optimal error, the conver- gence of the method is theoretically proved so that the P1 nonconforming quadrilateral element method can be applied more widely.

关 键 词：Oseen方程 涡旋粘性 非协调 四边形元 

分 类 号：O242.21[理学—计算数学]