A P2-P1 PARTIALLY PENALIZED IMMERSED FINITE ELEMENT METHOD FOR STOKES INTERFACE PROBLEMS
A P2-P1 PARTIALLY PENALIZED IMMERSED FINITE ELEMENT METHOD FOR STOKES INTERFACE PROBLEMS
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发表时间：
2021
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通讯作者：
Yuan Chen
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作者：
Yuan Chen
本文发展了一种求解二维Stokes界面问题的Taylor-Hood浸入有限元方法。利用最小二乘逼近构造了P2-P1局部IFE空间。采用带ghost惩罚的部分惩罚IFE方法求解斯托克界面问题。罚项施加在界面边缘和实际界面曲线上。为了提高数值格式的稳定性，特别是对于压力近似，采用了鬼罚项。在不同的界面形状和系数配置的各种数值实验中观察到的最佳收敛。通过数值实验研究了虚元和鬼罚的影响。
In this article, we develop a Taylor-Hood immersed finite element (IFE) method to solve two-dimensional Stokes interface problems. The P2-P1 local IFE spaces are constructed using the least-squares approximation on an enlarged fictitious element. The partially penalized IFE method with ghost penalty is employed for solving Stoke interface problems. Penalty terms are imposed on both interface edges and the actual interface curves. Ghost penalty terms are enforced to enhance the stability of the numerical scheme, especially for the pressure approximation. Optimal convergences are observed in various numerical experiments with different interface shapes and coefficient configurations. The effects of the ghost penalty and the fictitious element are also examined through numerical experiments.