Abstract: The Cahn-Hilliard equation which is a very important fourth-order diffusion model has profound physical background and rich theoretical connotation, and its numerical methods are of important scientific significance and engineering application value. In this paper, we develop and analyze the Discontinuous Galerkin (DG) finite element method for the fourth-order Cahn-Hilliard equation in one dimension. The method, which is different from the traditional local discontinuous Galerkin (LDG) method, can be applied without introducing any auxiliary variables or rewriting the original equation into a larger system and reduce the amount of computation and storage. We prove stability and convergence by choosing interface numerical fluxes carefully. Some numerical tests is provided to illustrate the accuracy and capability of the scheme.

Key words: Cahn-Hilliard equation, discontinuous Galerkin method, stability, error estimates