$C^1$ Virtual Element Method on polyhedral meshes
Numerical Analysis
2019-09-15 v3 Numerical Analysis
Abstract
The purpose of the present paper is to develop Virtual Elements in three dimensions for linear elliptic fourth order problems, motivated by the difficulties that standard conforming Finite Elements encounter in this framework. We focus the presentation on the lowest order case, the generalization to higher orders being briefly provided in the Appendix. The degrees of freedom of the proposed scheme are only 4 per mesh vertex, representing function values and gradient values. Interpolation error estimates for the proposed space are provided, together with a set of numerical tests to validate the method at the practical level.
Cite
@article{arxiv.1808.01105,
title = {$C^1$ Virtual Element Method on polyhedral meshes},
author = {Lourenco Beirão da Veiga and Franco Dassi and Alessandro Russo},
journal= {arXiv preprint arXiv:1808.01105},
year = {2019}
}
Comments
Computer & Mathematics with Applications (Jul 2019)