A new framework of high-order unfitted finite element methods using ALE maps for moving-domain problems
<|reference_start|>A new framework of high-order unfitted finite element methods using ALE maps for moving-domain problems: As a sequel to our previous work [C. Ma, Q. Zhang and W. Zheng, SIAM J. Numer. Anal., 60 (2022)], [C. Ma and W. Zheng, J. Comput. Phys. 469 (2022)], this paper presents a generic framework of arbitrary Lagrangian-Eulerian unfitted finite element (ALE-UFE) methods for partial differential equations (PDEs) on time-varying domains. The ALE-UFE method has a great potential in developing high-order unfitted finite element methods. The usefulness of the method is demonstrated by a variety of moving-domain problems, including a linear problem with explicit velocity of the boundary (or interface), a PDE-domain coupled problem, and a problem whose domain has a topological change. Numerical experiments show that optimal convergence is achieved by both third- and fourth-order methods on domains with smooth boundaries, but is deteriorated to the second order when the domain has topological changes.<|reference_end|>
@article{lu2024a,
    title={A new framework of high-order unfitted finite element methods using ALE
  maps for moving-domain problems},
    author={Wenhao Lu and Chuwen Ma and Weiying Zheng},
    journal={arXiv preprint arXiv:2404.15624},
    year={2024},
    archivePrefix={arXiv},
    eprint={2404.15624},
    primaryClass={math.NA cs.NA}
}