论文标题
表面Stokes方程的高阶痕量有限元方法的错误分析
Error analysis of higher order trace finite element methods for the surface Stokes equations
论文作者
论文摘要
该论文研究了在三维空间中在表面上构成的Stokes系统的高阶未有限元方法。该方法在四面体散装网格上采用了广义的泰勒 - 霍德元素对，以离散嵌入式表面上的Stokes系统。证明了稳定性和最佳订单收敛结果。证明包括完全量化了由于表面的近似参数表示所引起的几何误差。数值实验包括正式的收敛研究和单位球体上开尔文 - 螺旋不稳定性问题的示例。
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.
