A High-Order Conservative Cut Finite Element Method for Problems in Time-Dependent Domains
<|reference_start|>A High-Order Conservative Cut Finite Element Method for Problems in Time-Dependent Domains: A mass-conservative high-order unfitted finite element method for convection-diffusion equations in evolving domains is proposed. The space-time method presented in [P. Hansbo, M. G. Larson, S. Zahedi, Comput. Methods Appl. Mech. Engrg. 307 (2016)] is extended to naturally achieve mass conservation by utilizing Reynold's transport theorem. Furthermore, by partitioning the time-dependent domain into macroelements, a more efficient stabilization procedure for the cut finite element method in time-dependent domains is presented. Numerical experiments illustrate that the method fulfills mass conservation, attains high-order convergence, and the condition number of the resulting system matrix is controlled while sparsity is increased. Problems in bulk domains as well as coupled bulk-surface problems are considered.<|reference_end|>
@article{myrbäck2024a,
    title={A High-Order Conservative Cut Finite Element Method for Problems in
  Time-Dependent Domains},
    author={Sebastian Myrb"ack, Sara Zahedi},
    journal={arXiv preprint arXiv:2404.10756},
    year={2024},
    archivePrefix={arXiv},
    eprint={2404.10756},
    primaryClass={math.NA cs.NA}
}