Exploring High-order three dimensional Virtual Elements: bases and stabilizations

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 $p=10$). 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.

References in corpus (1)

• A multigrid algorithm for the $p$-version of the Virtual Element Method

Cited by in corpus (1)

• Non-conforming harmonic virtual element method: $h$- and $p$-versions