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.
出处
《数学物理学报（A辑）》
CSCD
北大核心
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
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
Stokes equations
Damped term
Nonconforming mixed elements
Superclose and superconvergence
Optimal error estimates
