Abstract Based on a fully overlapping domain decomposition approach, a parallel stabilized finite element variational multiscale method for the incompressible Navier-Stokes equations is proposed, where the stabilizations both for the velocity and pressure are based on two local Gauss integrations at the element level. The basic idea of the method is to use a locally refined global mesh to compute a stabilized solution in the given subdomain of interest. The proposed method only requires the application of an existing Navier-Stokes sequential solver on the locally refined global mesh associated with each subdomain, and thus can reuse the existing sequential solver without substantial recoding. Error bound of the approximate solutions from the proposed method is estimated with the use of local a priori error estimate for the stabilized solution. Algorithmic parameter scalings of the method are also derived. Some numerical simulations are presented to demonstrate the effectiveness of the method.

中文翻译：

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基于完全重叠域分解的不可压缩Navier-Stokes方程并行稳定有限元变分多尺度方法

摘要 基于完全重叠域分解方法，提出了不可压缩纳维-斯托克斯方程的并行稳定有限元变分多尺度方法，其中速度和压力的稳定均基于单元级的两个局部高斯积分。该方法的基本思想是使用局部细化的全局网格来计算给定感兴趣子域中的稳定解。所提出的方法只需要在与每个子域相关联的局部细化全局网格上应用现有的 Navier-Stokes 顺序求解器，因此可以重用现有的顺序求解器而无需大量重新编码。所提出的方法的近似解的误差界是通过使用稳定解的局部先验误差估计来估计的。还导出了该方法的算法参数缩放。给出了一些数值模拟来证明该方法的有效性。