Adapted Lie splitting method for convection-diffusion problems with singular convective term
<|reference_start|>Adapted Lie splitting method for convection-diffusion problems with singular convective term: Splitting methods are a widely used numerical scheme for solving convection-diffusion problems. However, they may lose stability in some situations, particularly when applied to convection-diffusion problems in the presence of an unbounded convective term. In this paper, we propose a new splitting method, called the "Adapted Lie splitting method", which successfully overcomes the observed instability in certain cases. Assuming that the unbounded coefficient belongs to a suitable Lorentz space, we show that the adapted Lie splitting converges to first-order under the analytic semigroup framework. Furthermore, we provide numerical experiments to illustrate our newly proposed splitting approach.<|reference_end|>
@article{dang2024adapted,
    title={Adapted Lie splitting method for convection-diffusion problems with
  singular convective term},
    author={Thi Tam Dang, Trung Hau Hoang, Giandomenico Orlandi},
    journal={arXiv preprint arXiv:2404.15947},
    year={2024},
    archivePrefix={arXiv},
    eprint={2404.15947},
    primaryClass={math.NA cs.NA}
}