This paper analyzes a parareal approach based on discontinuous Galerkin (DG) method for the time-dependent Stokes equations. A class of primal discontinuous Galerkin methods, namely variations of interior penalty methods, are adopted for the spatial discretization in the parareal algorithm (we call it parareal DG algorithm). We study three discontinuous Galerkin methods for the time-dependent Stokes equations, and the optimal continuous in time error estimates for the velocities and pressure are derived. Based on these error estimates, the proposed parareal DG algorithm is proved to be unconditionally stable and bounded by the error of discontinuous Galerkin discretization after a finite number of iterations. Finally, some numerical experiments are conducted which confirm our theoretical results, meanwhile, the efficiency of the parareal DG algorithm can be seen through a parallel experiment.

中文翻译：

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基于非连续Galerkin方法的时变Stokes方程的超现实方法分析

本文分析了一种基于不连续伽辽金(DG)方法的时间相关Stokes方程的超现实方法。超现实算法（我们称之为超现实DG算法）的空间离散化采用一类原始的不连续Galerkin方法，即内部惩罚方法的变体。我们研究了时间相关斯托克斯方程的三种不连续伽辽金方法，并得出了速度和压力的最佳连续时间误差估计。基于这些误差估计，证明了所提出的超现实 DG 算法是无条件稳定的，并且在有限次数的迭代后受到不连续 Galerkin 离散化误差的限制。最后，进行了一些数值实验，证实了我们的理论结果，同时，