A class of nonconforming immersed finite element methods for Stokes interface problems
A class of nonconforming immersed finite element methods for Stokes interface problems
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DOI：
10.1016/j.cam.2021.113493
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发表时间：
2021
期刊：
影响因子：
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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
本文介绍了一类求解二维Stokes界面问题的低阶非协调浸没有限元方法。所提出的方法不需要解网格与流体界面对齐，可以使用三角形网格或矩形网格。在三角形网格上，速度近似采用Crouzeix-Raviart单元，压力采用分段常数。在矩形网格上，采用Rannacher-Turek旋转Q1-Q0有限元。构造了新的矢量值IFE函数来逼近界面跳跃条件。讨论了这些新IFE函数的基本性质，包括不孤立性和单位分解。通过一系列数值算例，检验了新IFE空间对Stokes界面问题的逼近能力。观察到速度的L 2范数和破碎的H1范数以及压力的L 2范数的数值逼近是最优收敛的。
In this paper, we introduce a class of lowest-order nonconforming immersed finite element (IFE) methods for solving two-dimensional Stokes interface problems. The proposed methods do not require the solution mesh to align with the fluid interface and can use either triangular or rectangular meshes. On triangular meshes, the Crouzeix–Raviart element is used for velocity approximation, and piecewise constant for pressure. On rectangular meshes, the Rannacher–Turek rotated Q 1-Q 0 finite element is used. The new vector-valued IFE functions are constructed to approximate the interface jump conditions. Basic properties including the unisolvency and the partition of unity of these new IFE functions are discussed. Approximation capabilities of the new IFE spaces for the Stokes interface problems are examined through a series of numerical examples. Numerical approximations in the L 2-norm and the broken H 1-norm for the velocity and the L 2-norm for the pressure are observed to converge optimally.