An upwind DG scheme preserving the maximum principle for the convective Cahn-Hilliard model

@article{AcostaSoba2021AnUD,
  title={An upwind DG scheme preserving the maximum principle for the convective Cahn-Hilliard model},
  author={Daniel Acosta-Soba and Francisco Guill'en-Gonz'alez and Jos'e Rafael Rodr'iguez-Galv'an},
  journal={ArXiv},
  year={2021},
  volume={abs/2111.07313}
}
The design of numerical approximations of the Cahn-Hilliard model preserving the maximum principle is a challenging problem, even more if considering additional transport terms. In this work, we present a new upwind discontinuous Galerkin scheme for the convective Cahn-Hilliard model with degenerate mobility which preserves the maximum principle and prevents non-physical spurious oscillations. Furthermore, we show some numerical experiments in agreement with the previous theoretical results… 

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