We study the numerical solution of a Cahn-Hilliard/Allen-Cahn system with strong coupling through state and gradient dependent non-diagonal mobility matrices. A fully discrete approximation scheme in space and time is proposed which preserves the underlying gradient flow structure and leads to dissipation of the free-energy on the discrete level. Existence and uniqueness of the discrete solution is established and relative energy estimates are used to prove optimal convergence rates in space and time under minimal smoothness assumptions. Numerical tests are presented for illustration of the theoretical results and to demonstrate the viability of the proposed methods.

翻译：我们研究了一类通过状态和梯度依赖的非对角迁移矩阵实现强耦合的Cahn-Hilliard/Allen-Cahn系统的数值解。本文提出了一种全离散时空逼近格式，该格式保留了底层梯度流结构，并在离散层面上实现自由能耗散。建立了离散解的存在唯一性，并利用相对能量估计在最小光滑性假设下证明了时空最优收敛阶。通过数值算例对理论结果进行验证，并展示了所提方法的可行性。