A cutFEM divergence–free discretization for the stokes problem
A cutFEM divergence–free discretization for the stokes problem
复制标题
斯托克斯问题的 cutFEM 散度 — 自由离散化
DOI：
10.1051/m2an/2022072
复制
发表时间：
2023
期刊：
影响因子：
--
通讯作者：
Olshanskii, Maxim
中科院分区：
文献类型：
--
作者：
Liu, Haoran;Neilan, Michael;Olshanskii, Maxim
基于Scott-Vogelius对，我们构造并分析了Stokes问题的CutFEM离散化。离散分段多项式空间定义在宏单元三角剖分上，这些宏单元三角剖分不适合光滑的物理区域。边界条件imposedviapenalization通过帮助的Nitsch型离散化，而相对于小的和各向异性的削减的散装元件的稳定性是通过添加本地鬼罚款稳定条款。我们证明了该方案的稳定性以及边界O（h）邻域外的离散速度的无发散性。为了减轻由于违反无发散条件而引起的误差，我们引入了局部梯度-div稳定化。误差分析表明，grad-div参数可以像O（h−1）那样缩放，允许对违反质量守恒的惩罚相当重，同时仍然确保最优阶误差估计。
We construct and analyze a CutFEM discretization for the Stokes problem based on the Scott–Vogelius pair. The discrete piecewise polynomial spaces are defined on macro-element triangulations which are not fitted to the smooth physical domain. Boundary conditions are imposedviapenalization through the help of a Nitsche-type discretization, whereas stability with respect to small and anisotropic cuts of the bulk elements is ensured by adding local ghost penalty stabilization terms. We show stability of the scheme as well as a divergence–free property of the discrete velocity outside anO(h) neighborhood of the boundary. To mitigate the error caused by the violation of the divergence–free condition, we introduce local grad–div stabilization. The error analysis shows that the grad–div parameter can scale likeO(h−1), allowing a rather heavy penalty for the violation of mass conservation, while still ensuring optimal order error estimates.