Optimal error estimate of fully discrete HDG-IEQ scheme for the general type Cahn-Hilliard equation

In this article, we develop a linear, fully discrete numerical scheme for solving the fourth-order Cahn-Hilliard equation with the general type nonlinear potential, where spatial discretization is based on the hybridizable discontinuous Galerkin method, and the time discretization is based on the recently developed Invariant Energy Quadratization approach. The unconditional energy stability of the proposed scheme is proved rigorously. Further, the optimal unconditional error estimate of the fully discrete scheme is proved by using the error splitting technique. Some numerical examples are further performed to demonstrate the accuracy and efficiency of the scheme.