Poisson distribution

Finance

Statistics

Matrix (chemical analysis)

Monomial

Physics

Engineering

Mathematical analysis

Finite element method

Stiffness matrix

Eigenvalues and eigenvectors

Composite material

Economics

Political science

Order (exchange)

Materials science

Element (criminal law)

Pure mathematics

Applied mathematics

Mathematics

Quantum mechanics

Structural engineering

Condition number

Polynomial

Numerical Methods for Partial Differential Equations

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.

Ill‐conditioning in the virtual element method: Stabilizations and bases