Edge-averaged virtual element methods for convection-diffusion and convection-dominated problems
<|reference_start|>Edge-averaged virtual element methods for convection-diffusion and convection-dominated problems: This manuscript develops edge-averaged virtual element (EAVE) methodologies to address convection-diffusion problems effectively in the convection-dominated regime. It introduces a variant of EAVE that ensures monotonicity (producing an $M$-matrix) on Voronoi polygonal meshes, provided their duals are Delaunay triangulations with acute angles. Furthermore, the study outlines a comprehensive framework for EAVE methodologies, introducing another variant that integrates with the stiffness matrix derived from the lowest-order virtual element method for the Poisson equation. Numerical experiments confirm the theoretical advantages of the monotonicity property and demonstrate an optimal convergence rate across various mesh configurations.<|reference_end|>
@article{cao2024edge-averaged,
    title={Edge-averaged virtual element methods for convection-diffusion and
  convection-dominated problems},
    author={Shuhao Cao, Long Chen, Seulip Lee},
    journal={arXiv preprint arXiv:2402.13347},
    year={2024},
    archivePrefix={arXiv},
    eprint={2402.13347},
    primaryClass={math.NA cs.NA}
}