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We consider a time-stepping scheme of Crank-Nicolson type for the heatequation on a moving domain in Eulerian coordinates. As the spatial domainvaries between subsequent time steps, an extension of the solution from theprevious time step is required. Following Lehrenfeld \& Olskanskii [ESAIM:M2AN, 53(2):\,585-614, 2019], we apply an implicit extension based on so-calledghost-penalty terms. For spatial discretisation, a cut finite element method isused. We derive a complete a priori error analysis in space and time, whichshows in particular second-order convergence in time under a parabolic CFLcondition. Finally, we present numerical results in two and three spacedimensions that confirm the analytical estimates, even for much larger timesteps.

Analysis of an implicitly extended Crank-Nicolson scheme for the heat equation on a time-dependent domain