TY  - JOUR
AU  - Lee, Hyun Geun
PY  - 2025
TI  - An efficient and energy-stable scheme for the modified phase-field crystal equation with a strong nonlinear vacancy potential
JO  - AIMS Mathematics
SP  - 5568
EP  - 5582
VL  - 10
IS  - 3
AB  - 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.
UR  - https://doi.org/10.3934/math.2025257
DO  - 10.3934/math.2025257