The Crouzeix?Raviart element for the Stokes equations with the slip boundary condition on a curved boundary
The Crouzeix?Raviart element for the Stokes equations with the slip boundary condition on a curved boundary
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弯曲边界上具有滑移边界条件的 Stokes 方程的 Crouzeix?Raviart 元素
DOI：
10.1016/j.cam.2020.113123
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发表时间：
2021
影响因子：
2.4
通讯作者：
Kashiwabara Takahito
中科院分区：
文献类型：
--
作者：
Zhou Guanyu;Oikawa Issei;Kashiwabara Takahito
当曲边用多边形/多面体曲面逼近时，用连续离散速度来实现Stokes问题的滑移边界条件（SBC）可能会引起变分犯罪。为了避免变分犯罪，我们应用Crouzeix-Raviart（CR）元素离散SBC。在误差分析中，我们对经典插值进行了修正，使其满足离散SBC，并得到了插值误差。在考虑区域扰动的情况下，我们得到了一致性误差，并研究了二维和三维情形下收敛阶与外法向逼近之间的关系，得到了二维情形下的最优收敛性.然而，对于3D的情况下，我们的分析阐明，外法线近似可能会产生收敛速度的损失，这是由两个具体的插值例子证实。数值实验验证了理论分析的正确性。
When the curved boundary is approximated by a polygon/polyhedron’s surface, using a continuous discrete velocity to implement the slip boundary condition (SBC) of the Stokes problem may cause the variational crime. To avoid the variational crime, we apply the Crouzeix–Raviart (CR) element to discretize SBC. In error analysis, we modify the classical interpolation to satisfy the discrete SBC and obtain the interpolation error. Taking the domain perturbation into account, we derive the consistency error, and then investigate the relationship between the convergence order and the outer normal approximation for both 2D and 3D cases, where we obtain the optimal convergence for 2D cases. However, for 3D cases, our analysis elucidates that the outer normal approximation may yield a loss of the convergence rate, which is confirmed by two specific interpolation examples. The theoretical results are validated by numerical experiments.