Conforming/Non-conforming Virtual Elements and application to elasticity problems in curved three-dimensional domains
Numerical Analysis
2026-05-28 v1 Numerical Analysis
Abstract
The Virtual Element Method (VEM) is a well-established framework for solving partial differential equations on polygonal and polyhedral meshes. In this paper, we introduce a novel hybrid VEM that integrates both conforming and nonconforming virtual spaces. We apply this formulation to a three-dimensional linear elasticity problem, providing rigorous theoretical analysis to demonstrate optimal convergence rates. Furthermore, we explore the extension of this approach to domains with curved boundaries.
Cite
@article{arxiv.2605.28041,
title = {Conforming/Non-conforming Virtual Elements and application to elasticity problems in curved three-dimensional domains},
author = {L. Beirão da Veiga and F. Dassi and A. Russo and M. Trezzi},
journal= {arXiv preprint arXiv:2605.28041},
year = {2026}
}