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.
Dassi, F., Mascotto, L. (2018). Exploring high-order three dimensional virtual elements: Bases and stabilizations. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 75(9), 3379-3401 [10.1016/j.camwa.2018.02.005].
Exploring high-order three dimensional virtual elements: Bases and stabilizations
DASSI, FRANCO;MASCOTTO, LORENZO
2018
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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