Inf-sup stability of the trace $P_2-P_1$ Taylor-Hood elements for surface PDEs
Inf-sup stability of the trace $P_2-P_1$ Taylor-Hood elements for surface PDEs
复制标题
表面偏微分方程 $P_2-P_1$ 泰勒-胡德单元的 Inf-sup 稳定性
DOI：
10.1090/mcom/3551
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发表时间：
2020
影响因子：
2
通讯作者：
Zhiliakov, Alex
中科院分区：
文献类型：
--
作者：
Olshanskii, Maxim A.;Reusken, Arnold;Zhiliakov, Alex
本文研究了一种求解闭光滑曲面上Stokes方程组的几何非拟合有限元法，即迹有限元法或割有限元法。提出了一种基于标准Taylor-Hood（连续）体单元的迹有限元法。一个所谓的体积法向导数稳定，已知从文献中的跟踪有限元，是这种方法的一个重要组成部分。本文证明了迹-有限元对的inf-sup稳定性，其稳定常数关于离散参数和曲面在体网格中的位置一致有界。最优阶收敛的一致的变体的有限元遵循这个新的稳定性结果和插值性质的跟踪有限元。数值例子说明了该方法的性质。引用
The paper studies a geometrically unfitted finite element method (FEM), known as trace FEM or cut FEM, for the numerical solution of the Stokes system posed on a closed smooth surface. A trace FEM based on standard Taylor–Hood (continuous–) bulk elements is proposed. A so-called volume normal derivative stabilization, known from the literature on trace FEM, is an essential ingredient of this method. The key result proved in the paper is an inf-sup stability of the trace–finite element pair, with the stability constant uniformly bounded with respect to the discretization parameter and the position of the surface in the bulk mesh. Optimal order convergence of a consistent variant of the FEM follows from this new stability result and interpolation properties of the trace FEM. Properties of the method are illustrated with numerical examples. References