Finite element method coupled with multiscale finite element method for the non-stationary Stokes-Darcy model
<|reference_start|>Finite element method coupled with multiscale finite element method for the non-stationary Stokes-Darcy model: In this paper, we combine the multiscale flnite element method to propose an algorithm for solving the non-stationary Stokes-Darcy model, where the permeability coefflcient in the Darcy region exhibits multiscale characteristics. Our algorithm involves two steps: first, conducting the parallel computation of multiscale basis functions in the Darcy region. Second, based on these multiscale basis functions, we employ an implicitexplicit scheme to solve the Stokes-Darcy equations. One signiflcant feature of the algorithm is that it solves problems on relatively coarse grids, thus signiflcantly reducing computational costs. Moreover, under the same coarse grid size, it exhibits higher accuracy compared to standard flnite element method. Under the assumption that the permeability coefflcient is periodic and independent of time, this paper demonstrates the stability and convergence of the algorithm. Finally, the rationality and effectiveness of the algorithm are verifled through three numerical experiments, with experimental results consistent with theoretical analysis.<|reference_end|>
@article{hong2024finite,
    title={Finite element method coupled with multiscale finite element method for
  the non-stationary Stokes-Darcy model},
    author={Yachen Hong and Wenhan Zhang and Lina Zhao and Haibiao Zheng},
    journal={arXiv preprint arXiv:2403.11600},
    year={2024},
    archivePrefix={arXiv},
    eprint={2403.11600},
    primaryClass={math.NA cs.NA}
}