English

Structure-preserving weighted BDF2 methods for Anisotropic Cahn-Hilliard model: uniform/variable-time-steps

Numerical Analysis 2024-06-18 v2 Numerical Analysis

Abstract

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 GG-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.

Keywords

Cite

@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}
}
R2 v1 2026-06-28T16:00:31.470Z