A High-order Arbitrary Lagrangian-Eulerian Virtual Element Method for Convection-Diffusion Problems
<|reference_start|>A High-order Arbitrary Lagrangian-Eulerian Virtual Element Method for Convection-Diffusion Problems: A virtual element discretisation of an Arbitrary Lagrangian-Eulerian method for two-dimensional convection-diffusion equations is proposed employing an isoparametric Virtual Element Method to achieve higher-order convergence rates on curved edged polygonal meshes. The proposed method is validated with numerical experiments in which optimal $H^1$ and $L^2$ convergence are observed. This method is then successfully applied to an existing moving mesh algorithm for implicit moving boundary problems in which higher-order convergence is achieved.<|reference_end|>
@article{wells2024a,
    title={A High-order Arbitrary Lagrangian-Eulerian Virtual Element Method for
  Convection-Diffusion Problems},
    author={H. Wells},
    journal={arXiv preprint arXiv:2404.17661},
    year={2024},
    archivePrefix={arXiv},
    eprint={2404.17661},
    primaryClass={math.NA cs.NA}
}