Exploring high-order three dimensional virtual elements: Bases and stabilizations

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 p = 10). 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. (C) 2018 Elsevier Ltd. All rights reserved.