Unconditional convergence and superconvergence analysis for the transient Stokes equations with damping
Unconditional convergence and superconvergence analysis for the transient Stokes equations with damping
复制标题
带阻尼瞬态Stokes方程的无条件收敛和超收敛分析
DOI：
10.1016/j.amc.2020.125572
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发表时间：
2021
影响因子：
4
通讯作者：
Shi Dongyang
中科院分区：
文献类型：
--
作者：
Li Zhenzhen;Li Minghao;Shi Dongyang
本文给出了带阻尼项的瞬变Stokes方程的线性化后向Euler格式，其中速度和压力用最低阶Bernadi-Rauel矩形单元对来近似。利用Stokes算子和H∞1范数估计，得到了L∞(L 2)和L∞(H1)范数下速度和L−(L 2)范数下压力的无条件最优误差估计.此外，利用插值法后处理技术，得到了该方法的超逼近性质和全局超收敛结果。最后给出了一些数值结果，证实了理论分析的正确性。
In this paper, the linearized backward Euler scheme for the transient Stokes equations with damping is presented, in which the velocity and pressure are approximated by the lowest-order Bernadi-Raugel rectangular element pair. Unconditional optimal error estimates of the velocity in the norms L∞(L 2) and L∞(H 1), and the pressure in the norm L∞(L 2) are derived through the Stokes operator and the H− 1-norm estimate. Moreover, the superclose properties and global superconvergent results are obtained by the interpolation post-processing technique. Finally, some numerical results are provided to confirm the theoretical analysis.