带有阻尼项的定常Stokes方程的低阶非协调混合有限元方法的超逼近和超收敛分析  

Superclose and Superconvergence Analysis of a Low Order Nonconforming Mixed Finite Element Method for Stationary Stokes Equations with Damping

作　　者：石东洋[1] 于志云[2] 

机构地区：[1]郑州大学数学系,郑州450001 [2]中原工学院理学院,郑州450007

出　　处：《数学物理学报（A辑）》2013年第4期735-745,共11页Acta Mathematica Scientia

基　　金：国家自然科学基金(10671184;10971203;11271340);高等学校博士学科点专项科研基金(20094101110006);国家青年基金(11101384);河南省基础与前沿技术研究计划项目(122300410208)资助

摘　　要：用带约束的非协调旋转Q_1元和分片常数元来逼近定常的、不可压带有阻尼项的Stokes方程的速度和压力.证明了逼近解的存在惟一性.再利用精确解和逼近解的先验估计,并恰当选择参数α,v和r.得到了最优误差估计及超逼近结果.最后,通过插值后处理技术,导出了速度的H^1-模和压力L^2-模的O(h^2)阶的整体超收敛.In this paper,we apply the constrained nonconforming rotated Q_1 element and the piecewise constant element to approximate the velocity and the pressure for the stationary、 impressible Stokes equations with damped term,respectively.The existence and uniqueness of the approximated solutions are proved.Employing the prior estimates of the exact and approximate solutions and choosing the appropriate parameters α,v and r,the optimal error estimates and the superclose results are derived.Finally,the O(h^2) order global superconvergence in H^1-norm for the velocity and L^2-norm for the pressure is obtained by use of a postprocessing technique.

关 键 词：STOKES方程 阻尼项 非协调混合元 超逼近和超收敛 最优误差估计 

分 类 号：O241.2[理学—计算数学]