Two finite difference schemes for the phase field crystal equation |
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Authors: | HaiYan Cao ZhiZhong Sun |
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Institution: | 1. Department of Mathematics, Southeast University, Nanjing, 210096, China
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Abstract: | 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. |
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