JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2019, Vol. 54 ›› Issue (6): 118-126.doi: 10.6040/j.issn.1671-9352.0.2018.146

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Error analysis of a linearized Crank-Nicolson scheme for the phase field crystal equation

LI Juan   

  1. College of Jinshen, Nanjing Audit University, Nanjing 210023, Jiangsu, China
  • Published:2019-06-05

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Abstract: The phase field crystal model is a high order nonlinear evolutionary equation with the sixth order derivative in space. A linearized Crank-Nicolson scheme is presented. The scheme is explicit at the first-and second-time level. We just only to solve an implicit linearized scheme at the rest of the time level. In the derivation of the scheme, the nonlinear term (u3)xx is rewritten to be (3u2 ux)x, and then be discretized by central difference quotient. The priori estimate of the numerical solution and unconditional convergence is proved in L2 norm. The convergence order is two in time and space. Some numerical examples are presented to demonstrate the theoretical results.

Key words: phase field crystal equation, linearized Crank-Nicolson scheme, convergence, nonlinear problem, linearization

CLC Number: 

  • O241.82
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