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. Am...

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Bibliographic Details
Published in:Computers & mathematics with applications (1987) 2018-05, Vol.75 (9), p.3379-3401
Main Authors: Dassi, F., Mascotto, L.
Format: Article
Language:English
Subjects:
High-order methods
Ill-conditioned problems (mathematics)
Ill-conditioning
Mathematical analysis
Methods
Numerical analysis
Polyhedra
Polyhedral meshes
Polynomials
Robustness (mathematics)
Stiffness matrix
Virtual element method
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Summary: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.
ISSN:0898-1221
1873-7668
DOI:10.1016/j.camwa.2018.02.005