Exploring High-order three dimensional Virtual Elements: bases and stabilizations
Numerical Analysis
2017-09-14 v1
Abstract
We present numerical tests of the Virtual Element Method (VEM) tailored for the discretization of a three dimensional Poisson problem with high-order "polynomial" degree (up to ). Besides, we discuss possible reasons for which the method could return suboptimal-wrong error convergence curves. Among these motivations, we highlight ill-conditioning of the stiffness matrix and not particularly "clever" choices of the stabilizations. We propose variants of the definition of face/bulk degrees of freedom, as well as of stabilizations, which lead to methods that are much more robust in terms of numerical performances.
Cite
@article{arxiv.1709.04371,
title = {Exploring High-order three dimensional Virtual Elements: bases and stabilizations},
author = {Lorenzo Mascotto and Franco Dassi},
journal= {arXiv preprint arXiv:1709.04371},
year = {2017}
}