The phase field crystal (PFC) model is a nonlinear evolutionary equation that is of sixth order in space. In the first part of this work, we derive a three level linearized difference scheme, which is then proved to be energy stable, unique solvable and second order convergent in L 2 norm by the energy method combining with the inductive method. In the second part of the work, we analyze the unique solvability and convergence of a two level nonlinear difference scheme, which was developed by Zhang et al. in 2013. Some numerical results with comparisons are provided.
Keywordsphase field crystal model, nonlinear evolutionary equation, finite difference scheme, solvability, convergence
MSC(2010) 65M06, 65M12, 65M15Citation: Cao H Y, Sun Z Z. Two finite difference schemes for the phase field crystal equation.