$C^1$ virtual element methods on polygonal meshes with curved edges
<|reference_start|>$C^1$ virtual element methods on polygonal meshes with curved edges: In this work we design a novel $C^1$-conforming virtual element method of arbitrary order $k \geq 2$, to solve the biharmonic problem on a domain with curved boundary and internal curved interfaces in two dimensions. By introducing a suitable stabilizing form, we develop a rigorous interpolation, stability, and convergence analysis obtaining optimal error estimates in the energy norm. Finally, we validate the theoretical findings through numerical experiments.<|reference_end|>
@article{da veiga2024$c^1$,
    title={$C^1$ virtual element methods on polygonal meshes with curved edges},
    author={L. Beir~ao da Veiga, D. Mora and A. Silgado},
    journal={arXiv preprint arXiv:2408.17381},
    year={2024},
    archivePrefix={arXiv},
    eprint={2408.17381},
    primaryClass={math.NA cs.NA}
}