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The stabilized penalty-projection finite element method for the Navier-Stokes-Cahn-Hilliard-Oono system
Applied Numerical Mathematics ( IF 2.8 ) Pub Date : 2021-03-10 , DOI: 10.1016/j.apnum.2021.03.004
Xue Wang , Guang-an Zou , Bo Wang

In this paper, we propose the stabilized penalty-projection finite element method for solving the Navier-Stokes-Cahn-Hilliard-Oono system, which is used to simulate the movement of thrombus in the blood vessels. The proposed algorithms are based on mixed finite element method in spatial direction, combined with a backward-Euler scheme and penalty-projection scheme for temporal discretization. It is worth noting that the idea of introducing a stabilized term admits the energy laws of two fully discrete schemes. Moreover, the convergence error estimates for both the semi-discrete scheme and fully discrete schemes are established for the first time. Numerical experiments are also provided to verify our proposed methods, and to show the results of our schemes have good performance with the theoretical ones. Finally, the proposed schemes are successfully applied to study the movement status of thrombus in healthy and blocked arteries, respectively.



中文翻译:

Navier-Stokes-Cahn-Hilliard-Oono系统的稳定罚投影有限元方法

在本文中,我们提出了一种稳定的罚投影有限元方法来求解Navier-Stokes-Cahn-Hilliard-Oono系统,该方法用于模拟血栓在血管中的运动。提出的算法基于空间方向上的混合有限元方法,结合后向欧拉方案和惩罚投影方案进行时间离散化。值得注意的是,引入稳定项的想法承认了两种完全离散的方案的能量定律。此外,首次建立了半离散方案和完全离散方案的收敛误差估计。还提供了数值实验,以验证我们提出的方法,并证明我们的方案的结果与理论方法具有良好的性能。最后,

更新日期:2021-03-17
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