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

2017/09/13 by Mascotto, Lorenzo, Dassi, Franco · 3 citations
#65N12 #65N30 #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.1709.04371

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.

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• Towards a parallel Schwarz solver framework for virtual elements using GDSW coarse spaces
• Stabilization-free virtual element method for 2D third medium contact
• POLYDIM: A C++ library for POLYtopal DIscretization Methods

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