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. Finally, numerical comparisons with other schemes found in the literature are also carried out.

翻译：维护最大原则的Cahn-Hilliard模型数字近似值的设计是一个具有挑战性的问题,如果考虑更多的运输术语,甚至更为困难。在这项工作中,我们提出了一个新的上风不连续的Galerkin计划,用于对流的Cahn-Hilliard模型,该模型具有退化的流动性,保留了最大原则,并防止了非物理的虚假振荡。此外,我们展示了一些与先前的理论结果一致的数字实验。最后,还与文献中的其他方案进行了数字比较。