Structure preserving finite element schemes for the Navier-Stokes-Cahn-Hilliard system with degenerate mobility
<|reference_start|>Structure preserving finite element schemes for the Navier-Stokes-Cahn-Hilliard system with degenerate mobility: In this work we present two new numerical schemes to approximate the Navier-Stokes-Cahn-Hilliard system with degenerate mobility using finite differences in time and finite elements in space. The proposed schemes are conservative, energy-stable and preserve the maximum principle approximately (the amount of the phase variable being outside of the interval [0,1] goes to zero in terms of a truncation parameter). Additionally, we present several numerical results to illustrate the accuracy and the well behavior of the proposed schemes, as well as a comparison with the behavior of the Navier-Stokes-Cahn-Hilliard model with constant mobility.<|reference_end|>
@article{guillén-gonzález2024structure,
    title={Structure preserving finite element schemes for the
  Navier-Stokes-Cahn-Hilliard system with degenerate mobility},
    author={Francisco Guill'en-Gonz'alez and Giordano Tierra},
    journal={arXiv preprint arXiv:2405.14763},
    year={2024},
    archivePrefix={arXiv},
    eprint={2405.14763},
    primaryClass={math.NA cs.NA}
}