Stokes问题非协调有限元逼近的最大模估计  

MAXIMUM NORM ERROR ESTIMATES FOR NONCONFORMING FINITE ELEMENT APPROXIMATIONS OF STOKES PROBLEMS

作　　者：邓庆平[1] 沈树民[1] 

机构地区：[1]江苏省苏州市苏州大学数学系,215006

出　　处：《高校应用数学学报（A辑）》1993年第2期183-196,共14页Applied Mathematics A Journal of Chinese Universities(Ser.A)

摘　　要：本文考察了二维稳态和非稳态Stokes问题的基于速度—压力形式的非协调C-R逼近格式,利用Sobolev权模技巧和权模LBB条件,得到了稳态问题速度(包括它的梯度)和压力逼近解的拟最优的最大模估计,利用稳态问题结果和Stokes投影技巧,得到了非稳态问题速度(包括它的梯度)和压力的半离散逼近解的拟最优的最大模估计。This paper deals with the nonconforming C-R approximate schemes for velocity-pressure mixed formulations of the stationary and nonstationary Stokes problems in 2-D . The quasi-optimal maximum norm error estimates of approximate solutions of the stationary Stokes problem are obtained for the velocity, its gradient and the pressure fields, by means of Sobolev weighted norm method and weighted LBB condition. The quasi-optimal maximum error estimates of semidiscreted approximations of the nonstationary Stokes problem are derived for the velocity, its gradient and the pressure fields. Their proofs are based on some results of the stationary problem and the technique of Stokes projection.

关 键 词：非协调有限元 斯托克斯问题 逼近 

分 类 号：O357.1[理学—流体力学]