An unfitted Eulerian finite element method for the time-dependent Stokes problem on moving domains
An unfitted Eulerian finite element method for the time-dependent Stokes problem on moving domains
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DOI：
10.1093/imanum/drab044
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发表时间：
2020-02
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影响因子：
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通讯作者：
Henry von Wahl;T. Richter;C. Lehrenfeld
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文献类型：
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作者：
Henry von Wahl;T. Richter;C. Lehrenfeld
我们分析了一个欧拉有限元方法，结合欧拉时间步进计划适用于时间相关的Stokes方程与CutFEM方法使用inf-super稳定泰勒-胡德元素的空间离散。这是基于Leenfeld和Olshanskii（2019，时间相关域中PDE的欧拉有限元方法。ESAIM：M2 AN，53，585-614），并由Burman等人（2019，arXiv：1910.03054 [math.NA]）使用稳定的等阶元素扩展到移动域上的非平稳Stokes问题。分析包括通过在离散CutFEM设置中的近似水平集域上积分而产生的几何误差。该方法的实施和理论结果说明使用数值例子。
We analyse a Eulerian finite element method, combining a Eulerian time-stepping scheme applied to the time-dependent Stokes equations with the CutFEM approach using inf-sup stable Taylor–Hood elements for the spatial discretization. This is based on the method introduced by Lehrenfeld & Olshanskii (2019, A Eulerian finite element method for PDEs in time-dependent domains. ESAIM: M2AN, 53, 585–614) in the context of a scalar convection–diffusion problems on moving domains, and extended to the nonstationary Stokes problem on moving domains by Burman et al. (2019, arXiv:1910.03054 [math.NA]) using stabilized equal-order elements. The analysis includes the geometrical error made by integrating over approximated level set domains in the discrete CutFEM setting. The method is implemented and the theoretical results are illustrated using numerical examples.