An Error Analysis of a Numerical Scheme for the Cahn-Hilliard Equation Based on the Invariant Energy Quadratization Approach

A novel linear numerical scheme for the Cahn-Hilliard equation is constructed with the invariant energy quadratization approach. All nonlinear terms in this scheme are treated semi-explicitly and the resulting semi-discrete equation forms a linear system at each time step. It is proved that the proposed scheme is energy-stable unconditionally and solvable uniquely. The error estimate of the numerical scheme for the Cahn-Hilliard equation is discussed. Numerical examples show that the numerical solution of the linear numerical scheme basically achieves the second-order accuracy in the time direction and can effectively simulate the phase change process.