A Nonconforming Virtual Element Method for Advection-Diffusion-Reaction Problems with CIP Stabilization
<|reference_start|>A Nonconforming Virtual Element Method for Advection-Diffusion-Reaction Problems with CIP Stabilization: We study a nonconforming virtual element method (VEM) for advection-diffusion-reaction problems with continuous interior penalty (CIP) stabilization. The design of the method is based on a standard variational formulation of the problem (no skew-symmetrization), and boundary conditions are imposed with a Nitsche technique. We use the enhanced version of VEM, with a ``DoFi-DoFi'' stabilization in the diffusion and reaction terms. We prove stability of the proposed method and derive $h$-version error estimates.<|reference_end|>
@article{lovadina2024a,
    title={A Nonconforming Virtual Element Method for Advection-Diffusion-Reaction
  Problems with CIP Stabilization},
    author={Carlo Lovadina, Ilaria Perugia, Manuel Trezzi},
    journal={arXiv preprint arXiv:2407.00612},
    year={2024},
    archivePrefix={arXiv},
    eprint={2407.00612},
    primaryClass={math.NA cs.NA}
}