Abstract 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∞(L2) and L∞(H1), and the pressure in the norm L∞(L2) 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.

中文翻译：

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带阻尼瞬态Stokes方程的无条件收敛和超收敛分析

摘要 本文提出了具有阻尼的瞬态Stokes方程的线性化后向欧拉格式，其中速度和压力由最低阶Bernadi-Raugel矩形单元对近似。范数 L∞(L2) 和 L∞(H1) 中速度的无条件最优误差估计以及范数 L∞(L2) 中的压力是通过斯托克斯算子和 H − 1 范数估计得出的。此外，超接近性质和全局超收敛结果是通过插值后处理技术获得的。最后，提供了一些数值结果来证实理论分析。