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Error analysis of higher order trace finite element methods for the surface Stokes equation
Journal of Numerical Mathematics ( IF 3 ) Pub Date : 2020-10-04 , DOI: 10.1515/jnma-2020-0017
Thomas Jankuhn 1 , Maxim A. Olshanskii 2 , Arnold Reusken 1 , Alexander Zhiliakov 2
Affiliation  

The paper studies a higher order unfitted finite element method for the Stokes system posed on a surface in three-dimensional space. The method employs generalized Taylor-Hood finite element pairs on tetrahedral bulk mesh to discretize the Stokes system on embedded surface. Stability and optimal order convergence results are proved. The proofs include a complete quantification of geometric errors stemming from approximate parametric representation of the surface. Numerical experiments include formal convergence studies and an example of the Kelvin-Helmholtz instability problem on the unit sphere.

中文翻译:

曲面Stokes方程高阶迹有限元方法的误差分析

本文研究了三维空间曲面上Stokes系统的一种高阶未拟合有限元方法。该方法采用四面体体网格上的广义泰勒-胡德有限元对来离散嵌入表面上的斯托克斯系统。证明了稳定性和最优阶收敛结果。证明包括对源自表面近似参数表示的几何误差的完整量化。数值实验包括形式收敛研究和单位球面上开尔文-亥姆霍兹不稳定性问题的一个例子。
更新日期:2020-10-04
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