In this work we design a novel C1-conforming virtual element method of arbitrary order k≥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.
@article{arxiv.2408.17381,
title = {$C^1$ virtual element methods on polygonal meshes with curved edges},
author = {L. Beirão da Veiga and D. Mora and A. Silgado},
journal= {arXiv preprint arXiv:2408.17381},
year = {2025}
}