A key ingredient of our fictitious domain, higher order space-time cut finite element (CutFEM) approach for solving the incompressible Navier--Stokes equations on evolving domains (cf.\ \cite{Bause2021}) is the extension of the physical solution from the time-dependent flow domain $\Omega_f^t$ to the entire, time-independent computational domain $\Omega$. The extension is defined implicitly and, simultaneously, aims at stabilizing the discrete solution in the case of unavoidable irregular small cuts. Here, the convergence properties of the scheme are studied numerically for variations of the combined extension and stabilization.

翻译：我们虚构域中一个关键要素,即更高顺序的时空削减限量元素(CutFEM)(CutFEM),用于解决不断演变域中无法压缩的导航-斯托克斯方程式(参见\\\\ cite{Bause2021}),就是将物理解决方案从时间依赖流域$\ Omega_f ⁇ t扩大到整个时间独立的计算域$\Omega$。扩展是隐含定义的,同时,在不可避免的不规则小削减的情况下,旨在稳定离散解决方案。在此,对组合扩展和稳定性的变异,从数字上研究该计划的趋同性。