Convergence analysis of a nonconforming virtual element method for compressible miscible displacement problems in porous media
<|reference_start|>Convergence analysis of a nonconforming virtual element method for compressible miscible displacement problems in porous media: This article presents a priori error estimates of the miscible displacement of one compressible fluid by another in a porous medium. The study utilizes the $H(\rm div)$ conforming virtual element method (VEM) for the approximation of the velocity, while a non-conforming virtual element approach is employed for the concentration. The pressure is discretised using the standard piecewise discontinuous polynomial functions. These spatial discretization techniques are combined with a backward Euler difference scheme for time discretization. Error estimates are established for velocity, pressure and concentration. The article also includes numerical results that validate the theoretical estimates.<|reference_end|>
@article{kumar2024convergence,
    title={Convergence analysis of a nonconforming virtual element method for
  compressible miscible displacement problems in porous media},
    author={Sarvesh Kumar, Devika Shylaja},
    journal={arXiv preprint arXiv:2405.06352},
    year={2024},
    archivePrefix={arXiv},
    eprint={2405.06352},
    primaryClass={math.NA cs.NA}
}