A conforming-nonconforming mixed immersed finite element method for unsteady Stokes equations with moving interfaces
A conforming-nonconforming mixed immersed finite element method for unsteady Stokes equations with moving interfaces
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DOI：
10.3934/era.2021032
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发表时间：
2021
影响因子：
0.8
通讯作者：
Derrick Jones;Xu Zhang
中科院分区：
文献类型：
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作者：
Derrick Jones;Xu Zhang
本文对二维非定常Stokes界面问题提出了一种新的混合浸入有限元离散方法。建议的IFE空间使用协调线性元素的一个速度分量和非协调线性元素的其他速度分量。压力用分段常数近似。分析了新的向量值IFE函数的非独立性等基本性质。基于新的IFE空间，发展了求解具有静止或运动界面的非定常Stokes方程的半离散和全离散格式。在我们的数值方案中，不需要重新划分网格来解决移动界面问题。数值实验证明了这种新的IFE方法的性能。
In this article, we develop a new mixed immersed finite element discretization for two-dimensional unsteady Stokes interface problems with unfitted meshes. The proposed IFE spaces use conforming linear elements for one velocity component and non-conforming linear elements for the other velocity component. The pressure is approximated by piecewise constant. Unisolvency, among other fundamental properties of the new vector-valued IFE functions, is analyzed. Based on the new IFE spaces, semi-discrete and full-discrete schemes are developed for solving the unsteady Stokes equations with a stationary or a moving interface. Re-meshing is not required in our numerical scheme for solving the moving-interface problem. Numerical experiments are carried out to demonstrate the performance of this new IFE method.