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Development of Pressure-Robust Discontinuous Galerkin Finite Element Methods for the Stokes Problem
Journal of Scientific Computing ( IF 2.5 ) Pub Date : 2021-09-12 , DOI: 10.1007/s10915-021-01634-5
Lin Mu 1 , Xiu Ye 2 , Shangyou Zhang 3
Affiliation  

Pressure-robustness is an essential demand for the incompressible fluid simulation. In this paper, we develop the enhanced discontinuous Galerkin (DG) finite element methods for solving Stokes equations in the primary velocity-pressure formulation to achieve pressure-robustness. The velocity reconstruction operator has been designed for discontinuous functions and utilized to modify the external source assembling. The new schemes stay almost the same as that in the existing DG schemes but only differ for the source terms. The conforming discontinuous Galerkin and symmetric interior penalty DG have been employed to demonstrate the enhancement. Optimal-order error estimates are established for the corresponding numerical approximation in various norms. Several numerical experiments are performed to validate our theoretical conclusions.



中文翻译:

解决斯托克斯问题的压力鲁棒性不连续伽辽金有限元方法的发展

压力稳健性是不可压缩流体模拟的基本要求。在本文中,我们开发了增强型不连续伽辽金 (DG) 有限元方法,用于求解初级速度-压力公式中的斯托克斯方程,以实现压力稳健性。速度重建算子是为不连续函数设计的,用于修改外部源组装。新方案与现有 DG 方案几乎相同,但仅在来源条款上有所不同。一致的不连续伽辽金和对称内罚 DG 已被用来证明增强。为各种范数中的相应数值近似建立了最优阶误差估计。进行了几个数值实验来验证我们的理论结论。

更新日期:2021-09-12
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