An efficient and energy-stable scheme for the modified phase-field crystal equation with a strong nonlinear vacancy potential
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 treate...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2025-03-01
|
| Series: | AIMS Mathematics |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2025257 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | 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. |
|---|---|
| ISSN: | 2473-6988 |