Convergence analysis of a second order convex splitting scheme for the modified phase field crystal equation (Q2870630)

The paper under review deals with the convergence analysis for an unconditionally energy stable, second-order accurate convex splitting scheme for the modified phase field crystal equation, a generalized damped wave equation for which the usual phase field crystal equation is a special degenerate case. A basic idea in this analysis is the introduction of a new variable \(\psi\), which corresponds to the temporal derivative of the phase variable. This provides an accuracy reduction in the formal consistency estimate, because of the hyperbolic nature of the equation. In the second part of this paper, the second order convergence in both time and space is established in a discrete \(L^\infty (0,T; H^3)\) norm.