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 en...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,uniquely 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.展开更多
基金supported by National Natural Science Foundation of China(Grant No.11271068)
文摘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,uniquely 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.
