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Error estimates for second-order SAV finite element method to phase field crystal model

  • Received: 01 March 2020 Revised: 01 July 2020 Published: 25 August 2020
  • Primary, 65M12, 65M60, 35Q56

  • In this paper, the second-order scalar auxiliary variable approach in time and linear finite element method in space are employed for solving the Cahn-Hilliard type equation of the phase field crystal model. The energy stability of the fully discrete scheme and the boundedness of numerical solution are studied. The rigorous error estimates of order $ O(\tau^2+h^2) $ in the sense of $ L^2 $-norm is derived. Finally, some numerical results are given to demonstrate the theoretical analysis.

    Citation: Liupeng Wang, Yunqing Huang. Error estimates for second-order SAV finite element method to phase field crystal model[J]. Electronic Research Archive, 2021, 29(1): 1735-1752. doi: 10.3934/era.2020089

    Related Papers:

  • In this paper, the second-order scalar auxiliary variable approach in time and linear finite element method in space are employed for solving the Cahn-Hilliard type equation of the phase field crystal model. The energy stability of the fully discrete scheme and the boundedness of numerical solution are studied. The rigorous error estimates of order $ O(\tau^2+h^2) $ in the sense of $ L^2 $-norm is derived. Finally, some numerical results are given to demonstrate the theoretical analysis.



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