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 \emph{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.
翻译:在本文中,我们为Cahn-Hilliard等式引入了新型的不连续的Galerkin(DG)计划(DG)计划(DG),它在许多应用中产生。该方法的设计方法是将空间分解的DG混合法与时间分解法(IEQ ) 相结合。 与空间预测相结合,由此形成的IEQ-DG计划被证明是无条件的能源分解,并且可以在不诉诸任何迭代法的情况下有效地解决。 提供了一、二维的数值示例来验证理论结果,并展示了IEQ-D在效率、准确性和维护理想解决方案属性方面的良好表现。