Superconvergence error estimates for the div least-squares finite element method on elliptic problems
<|reference_start|>Superconvergence error estimates for the div least-squares finite element method on elliptic problems: In this paper we discuss the error estimations for the div least-squares finite element method on elliptic problems. Compared with the previous work, we present a complete error analysis, which improves the current \emph{state-of-the-art} results. The error estimations for both the scalar and the flux variables are established by dual arguments, and in most cases, only an $H^{1+\varepsilon}$ regularity is used. Numerical experiments strongly confirm our analysis.<|reference_end|>
@article{chen2024superconvergence,
    title={Superconvergence error estimates for the div least-squares finite
  element method on elliptic problems},
    author={Gang Chen, Fanyi Yang, Zheyuan Zhang},
    journal={arXiv preprint arXiv:2404.04918},
    year={2024},
    archivePrefix={arXiv},
    eprint={2404.04918},
    primaryClass={math.NA cs.NA}
}