An improved error analysis for a second-order numerical scheme for the Cahn–Hilliard equation

In this paper we present an error analysis for a second order accurate numerical scheme the 2-D and 3-D Cahn–Hilliard (CH) equation, with improved convergence constant. The unique solvability, unconditional energy stability, uniform-in-time H2 stability of have already been established. However, standard estimate gives constant in exp(CT??m0), m0 positive integer interface width parameter ? being small, which comes from application discrete Gronwall inequality. To overcome well-known difficulty, apply spectrum linearized operator (Alikakos Fusco, 1993; Chen, 1994; Feng Prohl, 2004), perform detailed analysis, get estimate, depends on 1? only polynomial order, instead exponential order.