On the Superconvergence of a Hybridizable Discontinuous Galerkin Method for the Cahn-Hilliard Equation.

We propose a hybridizable discontinuous Galerkin (HDG) method with the convex -concave splitting temporal discretization for solving the Cahn-Hilliard equation. We establish opti-mal convergence rates for the scalar variables and the flux variables in the L2 norm for polynomials of degree k \geq 0. The error constants depend on inverse of the interface thickness in polynomial orders, which is obtained by utilizing a spectral-type estimate of the discrete Cahn-Hilliard opera-tor in the HDG framework. In terms of degrees of freedom of the globally coupled unknowns, the scalar variables are superconvergent. Numerical results are reported to corroborate the theoretical convergence rates and the effectiveness of the method.