JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2021, Vol. 56 ›› Issue (12): 17-25.doi: 10.6040/j.issn.1671-9352.0.2021.327

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Finite element method of Cahn-Hilliard equation based on adaptive moving mesh method

LU Chang-na, CHANG Sheng-xiang   

  1. College of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, Jiangsu, China
  • Published:2021-11-25

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Abstract: A finite element method is proposed for the two-dimensional Cahn-Hilliard equation based on the adaptive moving mesh. Since the Cahn-Hilliard equation changes rapidly in the initial stage and slowly changes in the later stage, the use of the moving mesh rule based on the moving mesh partial differential equation(MMPDE)can better capture the phase diagram. The method is discretized by using linear finite element in space and fifth-order Radau IIA scheme in time. Numerical results shows that the numerical solution can well maintain the law of conservation of mass and the law of energy stability, and improve the calculation efficiency, which verifies the effectiveness and feasibility of the method.

Key words: linear finite element, adaptive moving mesh, Cahn-Hilliard equation, energy stability

CLC Number: 

  • O242.21
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