A Cahn-Hilliard-Allen-Cahn phase-field model coupled with a heat transfer equation, particularly with full non-diagonal mobility matrices, is studied. After reformulating the problem w.r.t. the inverse of temperature, we proposed and analysed a structure-preserving approximation for the semi-discretisation in space and then a fully discrete approximation using conforming finite elements and time-stepping methods. We prove structure-preserving property and discrete stability using relative entropy methods for the semi-discrete and fully discrete case. The theoretical results are illustrated by numerical experiments.

翻译：研究了一个与热传导方程耦合的Cahn-Hilliard-Allen-Cahn相场模型，特别考虑了完全非对角迁移率矩阵的情况。在将问题相对于温度的倒数重新表述后，提出并分析了一种空间半离散化的结构保持近似，随后采用协调有限元和时间步进方法得到了全离散近似。利用相对熵方法证明了半离散和全离散情况下的结构保持性质与离散稳定性。数值实验验证了理论结果。