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Efficient Fully Discrete Finite-Element Numerical Scheme with Second-Order Temporal Accuracy for the Phase-Field Crystal Model

Author

Listed:
  • Jun Zhang

    (Guizhou Key Laboratory of Big Data Statistical Analysis, Guizhou University of Finance and Economics, Guiyang 550025, China)

  • Xiaofeng Yang

    (Department of Mathematics, University of South Carolina, Columbia, SC 29208, USA)

Abstract

In this paper, we consider numerical approximations of the Cahn–Hilliard type phase-field crystal model and construct a fully discrete finite element scheme for it. The scheme is the combination of the finite element method for spatial discretization and an invariant energy quadratization method for time marching. It is not only linear and second-order time-accurate, but also unconditionally energy-stable. We prove the unconditional energy stability rigorously and further carry out various numerical examples to demonstrate the stability and the accuracy of the developed scheme numerically.

Suggested Citation

  • Jun Zhang & Xiaofeng Yang, 2022. "Efficient Fully Discrete Finite-Element Numerical Scheme with Second-Order Temporal Accuracy for the Phase-Field Crystal Model," Mathematics, MDPI, vol. 10(1), pages 1-11, January.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:1:p:155-:d:717955
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