The mixed form of the Cahn-Hilliard equations is discretized by the hybridizable 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-Lindau 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.

翻译：采用杂交化间断伽辽金方法对Cahn-Hilliard方程的混合形式进行离散。对于任意化学能密度，数值解的存在唯一性得以建立。该方案被证明是无条件稳定的。通过推导先验误差估计，获得了适用于Ginzburg-Lindau化学能密度及凸区域的方法收敛性。本文还包含离散泛函工具，即在杂交化间断伽辽金空间中证明成立的离散Agmon不等式与Gagliardo-Nirenberg不等式。