In this paper, we introduce novel discontinuous Galerkin (DG) schemes for the Cahn-Hilliard equation, which arises in many applications. The method is designed by integrating the mixed DG method for the spatial discretization with the Invariant Energy Quadratization (IEQ) approach for the time discretization. Coupled with a spatial projection, the resulting IEQ-DG schemes are shown to be unconditionally energy dissipative, and can be efficiently solved without resorting to any iteration method. Both one and two dimensional numerical examples are provided to verify the theoretical results, and demonstrate the good performance of IEQ-DG in terms of efficiency, accuracy, and preservation of the desired solution properties.

在本文中，我们为Cahn-Hilliard方程引入了新颖的不连续Galerkin（DG）方案，这种方案在许多应用中都出现了。该方法是通过将用于空间离散化的混合DG方法与用于时间离散化的不变能量平方（IEQ）方法集成在一起而设计的。结合空间投影，所得的IEQ-DG方案显示为无条件耗能的，可以有效地解决而无需借助任何迭代方法。提供了一维和二维数值示例来验证理论结果，并证明IEQ-DG在效率，准确性和所需溶液性质的保留方面均具有良好的性能。