• Ill-conditioning in the virtual element method: Stabilizations and bases

  • 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.

  • PDF

  • http://phaidra.univie.ac.at/o:1005829

  • Article

  • Published Version

  • 2018

  • 34

  • 4

  • 1258-1281

  • Wiley

  • English

  • Open access

  • CC BY Attribution 4.0 International
    © 2018 The Authors

  • 0749-159X

  • virtual element methods; hp Galerkin methods; Ill‐conditioning