A fitted space-time finite element method for an advection-diffusion problem with moving interfaces
<|reference_start|>A fitted space-time finite element method for an advection-diffusion problem with moving interfaces: This paper presents a fitted space-time finite element method for solving a parabolic advection-diffusion problem with a nonstationary interface. The jumping diffusion coefficient gives rise to the discontinuity of the spatial gradient of solution across the interface. We use the Banach-Necas-Babuska theorem to show the well-posedness of the continuous variational problem. A fully discrete finite-element based scheme is analyzed using the Galerkin method and unstructured fitted meshes. An optimal error estimate is established in a discrete energy norm under appropriate globally low but locally high regularity conditions. Some numerical results corroborate our theoretical results.<|reference_end|>
@article{nguyen2024a,
    title={A fitted space-time finite element method for an advection-diffusion
  problem with moving interfaces},
    author={Quang Huy Nguyen, Van Chien Le, Phuong Cuc Hoang, Thi Thanh Mai Ta},
    journal={arXiv preprint arXiv:2407.08439},
    year={2024},
    archivePrefix={arXiv},
    eprint={2407.08439},
    primaryClass={math.NA cs.NA}
}