A construction of canonical nonconforming finite element spaces for elliptic equations of any order in any dimension
<|reference_start|>A construction of canonical nonconforming finite element spaces for elliptic equations of any order in any dimension: A unified construction of canonical $H^m$-nonconforming finite elements is developed for $n$-dimensional simplices for any $m, n \geq 1$. Consistency with the Morley-Wang-Xu elements [Math. Comp. 82 (2013), pp. 25-43] is maintained when $m \leq n$. In the general case, the degrees of freedom and the shape function space exhibit well-matched multi-layer structures that ensure their alignment. Building on the concept of the nonconforming bubble function, the unisolvence is established using an equivalent integral-type representation of the shape function space and by applying induction on $m$. The corresponding nonconforming finite element method applies to $2m$-th order elliptic problems, with numerical results for $m=3$ and $m=4$ in 2D supporting the theoretical analysis.<|reference_end|>
@article{li2024a,
    title={A construction of canonical nonconforming finite element spaces for
  elliptic equations of any order in any dimension},
    author={Jia Li, Shuonan Wu},
    journal={arXiv preprint arXiv:2409.06134},
    year={2024},
    archivePrefix={arXiv},
    eprint={2409.06134},
    primaryClass={math.NA cs.NA}
}