@article{Lee2025, 
author = {Hyun Geun Lee},
title = {An efficient and energy-stable scheme for the modified phase-field crystal equation with a strong nonlinear vacancy potential},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {3},
pages = {5568-5582},
keywords = {modified phase-field crystal equation, strong nonlinear vacancy potential, efficiency, energy stability},
url = {https://www.sciopen.com/article/10.3934/math.2025257},
doi = {10.3934/math.2025257},
abstract = {In this paper, we present an efficient and energy-stable scheme based on the Crank–Nicolson formula for the modified phase-field crystal equation with a strong nonlinear vacancy potential. In the scheme, the nonlinear terms (the first derivatives of the double-well and vacancy potentials) are treated explicitly, which makes the scheme efficient, and the energy stability is guaranteed by assuming that the second derivatives of the double-well and vacancy potentials are each bounded and by adding two second-order stabilization terms. In particular, by bounding the second derivatives of the double-well and vacancy potentials, respectively, we can choose the stabilization parameters independently of the vacancy parameter. As a result, the convergence constant and energy decay trend are not affected by the vacancy parameter.}
}