Structure-preserving weighted BDF2 methods for Anisotropic Cahn-Hilliard model: uniform/variable-time-steps
数值分析
2024-06-18 v2 数值分析
摘要
In this paper, we innovatively develop uniform/variable-time-step weighted and shifted BDF2 (WSBDF2) methods for the anisotropic Cahn-Hilliard (CH) model, combining the scalar auxiliary variable (SAV) approach with two types of stabilized techniques. Using the concept of -stability, the uniform-time-step WSBDF2 method is theoretically proved to be energy-stable. Due to the inapplicability of the relevant G-stability properties, another technique is adopted in this work to demonstrate the energy stability of the variable-time-step WSBDF2 method. In addition, the two numerical schemes are all mass-conservative.Finally, numerous numerical simulations are presented to demonstrate the stability and accuracy of these schemes.
引用
@article{arxiv.2404.13259,
title = {Structure-preserving weighted BDF2 methods for Anisotropic Cahn-Hilliard model: uniform/variable-time-steps},
author = {Meng Li and Jingjiang Bi and Nan Wang},
journal= {arXiv preprint arXiv:2404.13259},
year = {2024}
}