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We analyse a Eulerian Finite Element method, combining a Euleriantime-stepping scheme applied to the time-dependent Stokes equations using theCutFEM approach with inf-sup stable Taylor-Hood elements for the spatialdiscretisation. This is based on the method introduced by Lehrenfeld \&Olshanskii [ESAIM: M2AN 53(2):585--614] in the context of a scalarconvection-diffusion problems on moving domains, and extended to thenon-stationary Stokes problem on moving domains by Burman, Frei \& Massing[arXiv:1910.03054 [math.NA]] using stabilised equal-order elements. Theanalysis includes the geometrical error made by integrating over approximatedlevelset domains in the discrete CutFEM setting. The method is implemented andthe theoretical results are illustrated using numerical examples.

An unfitted Eulerian finite element method for the time-dependent Stokes problem on moving domains