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A key ingredient of our fictitious domain, higher order space-time cut finiteelement (CutFEM) approach for solving the incompressible Navier--Stokesequations on evolving domains (cf.\ \cite{Bause2021}) is the extension of thephysical solution from the time-dependent flow domain $\Omega_f^t$ to theentire, time-independent computational domain $\Omega$. The extension isdefined implicitly and, simultaneously, aims at stabilizing the discretesolution in the case of unavoidable irregular small cuts. Here, the convergenceproperties of the scheme are studied numerically for variations of the combinedextension and stabilization.

Numerical convergence of discrete extensions in a space-time finite element, fictitious domain method for the Navier-Stokes equations