Space-Time Aggregated Finite Element Methods for Time-Dependent Problems on Moving Domains

  • Badia, Santiago (Monash University)
  • Dilip, Hridya (Monash University)
  • Verdugo, Francesc (VU Amsterdam)

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We propose a space-time scheme that combines an unfitted finite element method in space with a discontinuous Galerkin time discretisation for the accurate numerical approximation of parabolic problems with moving domains or interfaces. We make use of an aggregated finite element space to attain robustness with respect to the cut locations. The aggregation is performed slab-wise to have a tensor product structure of the space-time discrete space, yielding optimal error estimates. We analyse the proposed algorithm, providing stability, condition number bounds and anisotropic a priori error estimates. We also present a set of numerical experiments that confirm the theoretical results for a parabolic problem on a moving domain. Moreover, we apply the method for a mass transfer problem with changing topology. We observe that the method is robust and accurate for all numerical simulations.