Stable Liftings of Polynomial Traces on Tetrahedra
<|reference_start|>Stable Liftings of Polynomial Traces on Tetrahedra: On the reference tetrahedron $K$, we construct, for each $k \in \mathbb{N}_0$, a right inverse for the trace operator $u \mapsto (u, \partial_{n} u, \ldots, \partial_{n}^k u)|_{\partial K}$. The operator is stable as a mapping from the trace space of $W^{s, p}(K)$ to $W^{s, p}(K)$ for all $p \in (1, \infty)$ and $s \in (k+1/p, \infty)$. Moreover, if the data is the trace of a polynomial of degree $N \in \mathbb{N}_0$, then the resulting lifting is a polynomial of degree $N$. One consequence of the analysis is a novel characterization for the range of the trace operator.<|reference_end|>
@article{parker2024stable,
    title={Stable Liftings of Polynomial Traces on Tetrahedra},
    author={Charles Parker and Endre S"uli},
    journal={arXiv preprint arXiv:2402.15789},
    year={2024},
    archivePrefix={arXiv},
    eprint={2402.15789},
    primaryClass={math.NA cs.NA}
}