Energy-stable parametric finite element approximations for regularized solid-state dewetting in strongly anisotropic materials
<|reference_start|>Energy-stable parametric finite element approximations for regularized solid-state dewetting in strongly anisotropic materials: In this work, we aim to develop energy-stable parametric finite element approximations for a sharp-interface model with strong surface energy anisotropy, which is derived from the first variation of an energy functional composed of film/vapor interfacial energy, substrate energy, and regularized Willmore energy. By introducing two geometric relations, we innovatively establish an equivalent regularized sharp-interface model and further construct an energy-stable parametric finite element algorithm for this equivalent model. We provide a detailed proof of the energy stability of the numerical scheme, addressing a gap in the relevant theory. Additionally, we develop another structure-preserving parametric finite element scheme that can preserve both area conservation and energy stability. Finally, we present several numerical simulations to show accuracy and efficiency as well as some structure-preserving properties of the proposed numerical methods. More importantly, extensive numerical simulations reveal that our schemes provide better mesh quality and are more suitable for long-term computations.<|reference_end|>
@article{li2024energy-stable,
    title={Energy-stable parametric finite element approximations for regularized
  solid-state dewetting in strongly anisotropic materials},
    author={Meng Li and Chunjie Zhou},
    journal={arXiv preprint arXiv:2407.04524},
    year={2024},
    archivePrefix={arXiv},
    eprint={2407.04524},
    primaryClass={math.NA cs.NA}
}