Two and three dimensional $H^2$-conforming finite element approximations without $C^1$-elements
<|reference_start|>Two and three dimensional $H^2$-conforming finite element approximations without $C^1$-elements: We develop a method to compute $H^2$-conforming finite element approximations in both two and three space dimensions using readily available finite element spaces. This is accomplished by deriving a novel, equivalent mixed variational formulation involving spaces with at most $H^1$-smoothness, so that conforming discretizations require at most $C^0$-continuity. The method is demonstrated on arbitrary order $C^1$-splines.<|reference_end|>
@article{ainsworth2024two,
    title={Two and three dimensional $H^2$-conforming finite element approximations
  without $C^1$-elements},
    author={Mark Ainsworth and Charles Parker},
    journal={arXiv preprint arXiv:2406.00338},
    year={2024},
    archivePrefix={arXiv},
    eprint={2406.00338},
    primaryClass={math.NA cs.NA}
}