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Titel
Ill-conditioning in the virtual element method: Stabilizations and bases
Abstract
In this article, we investigate the behavior of the condition number of the stiffness matrix resulting from the approximation of a 2D Poisson problem by means of the virtual element method. It turns out that ill‐conditioning appears when considering high‐order methods or in presence of “bad‐shaped” (for instance nonuniformly star‐shaped, with small edges…) sequences of polygons. We show that in order to improve such condition number one can modify the definition of the internal moments by choosing proper polynomial functions that are not the standard monomials. We also give numerical evidence that at least for a 2D problem, standard choices for the stabilization give similar results in terms of condition number.
Objekt-Typ
Sprache
Englisch [eng]
Stichwort
virtual element methodshp Galerkin methodsIll‐conditioning
Erscheinungsdatum
2018
Seitenanfang
1258
Seitenende
1281
Erschienen in
Titel
Numerical Methods for Partial Differential Equations
Band
34
Ausgabe
4
Verlag
Wiley
Persistent identifier
https://phaidra.univie.ac.at/o:1005829
Zugänglichkeit
Rechteangabe
© 2018 The Authors

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