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

摘要/Abstract

摘要：

用带约束的非协调旋转Q₁ 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, ν 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H¹ -模和压力 L² -模的O(h²)阶的整体超收敛.

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

Abstract:

In this paper, we apply the constrained nonconforming rotated Q₁element 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, ν and r, the optimal error estimates and the superclose results are derived. Finally, the O(h²) order global superconvergence in H¹-norm for the velocity and L²-norm for the pressure is obtained by use of a postprocessing technique.

Key words: Stokes equations, Damped term, Nonconforming mixed elements, Superclose and superconvergence, Optimal error estimates

中图分类号:

65N30

石东洋, 于志云. 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[J]. 数学物理学报, 2013, 33(4): 735-745.

SHI Dong-Yang, YU Zhi-Yun. Superclose and Superconvergence Analysis of a Low Order Nonconforming Mixed Finite Element Method for Stationary
Stokes Equations with Damping[J]. Acta mathematica scientia,Series A, 2013, 33(4): 735-745.

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