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

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