The mixed form of the Cahn–Hilliard equations is discretized by the hybridized discontinuous Galerkin method. For any chemical energy density, existence and uniqueness of the numerical solution is obtained. The scheme is proved to be unconditionally stable. Convergence of the method is obtained by deriving a priori error estimates that are valid for the Ginzburg–Landau chemical energy density and for convex domains. The paper also contains discrete functional tools, namely discrete Agmon and Gagliardo–Nirenberg inequalities, which are proved to be valid in the hybridizable discontinuous Galerkin spaces.

中文翻译：

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Cahn-Hilliard 问题的混合间断 Galerkin 方法的数值分析

Cahn-Hilliard 方程的混合形式通过混合间断伽辽金法进行离散化。对于任何化学能量密度，都得到数值解的存在性和唯一性。证明该方案是无条件稳定的。该方法的收敛性是通过推导对 Ginzburg-Landau 化学能量密度和凸域有效的先验误差估计来获得的。该论文还包含离散函数工具，即离散 Agmon 和 Gagliardo-Nirenberg 不等式，它们被证明在可杂交不连续 Galerkin 空间中有效。