Abstract This paper presents the new error estimates for a second-order backward-differentiation scheme (BDF2) given in [3] for the evolutionary Stokes-Darcy system. We prove the unconditional optimal error estimates and the uniform in time error estimates with the modest time step ( Δ t ≤ C ) for the fluid velocity and the hydraulic head in L 2 norm. Besides, we also prove the error estimates for the fluid velocity and the hydraulic head in H 1 norm are Δ t 15 8 + h and the pressures in L 2 norms are Δ t 7 4 + h . Numerical tests are provided to illustrate the accuracy and validity of the decoupled scheme.

中文翻译：

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进化Stokes-Darcy系统二阶解耦方案的误差估计

摘要 本文介绍了 [3] 中给出的用于进化斯托克斯-达西系统的二阶后向微分方案 (BDF2) 的新误差估计。我们证明了在 L 2 范数下，对于流体速度和水头的无条件最优误差估计和具有适度时间步长 (Δ t ≤ C ) 的均匀时间误差估计。此外，我们还证明了H 1 范数中流体速度和水头的误差估计为Δ t 15 8 + h ，L 2 范数中的压力为Δ t 7 4 + h 。提供了数值测试来说明解耦方案的准确性和有效性。