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We propose a space-time scheme that combines an unfitted finite elementmethod in space with a discontinuous Galerkin time discretisation for theaccurate numerical approximation of parabolic problems with moving domains orinterfaces. We make use of an aggregated finite element space to attainrobustness with respect to the cut locations. The aggregation is performedslab-wise to have a tensor product structure of the space-time discrete space,which is required in the numerical analysis. We analyse the proposed algorithm,providing stability, condition number bounds and anisotropic \emph{a priori}error estimates. A set of numerical experiments confirm the theoretical resultsfor a parabolic problem on a moving domain. The method is applied for a masstransfer problem with changing topology.

Space-time unfitted finite element methods for time-dependent problems on moving domains