Virtual element approximation of eigenvalue problems: is the stabilization of the right hand side necessary?
Numerical Analysis
2026-04-07 v1 Numerical Analysis
Abstract
The VEM approximation of eigenvalue problems usually involves the appropriate tuning of stabilization parameters, unless self-stabilizing or stabilization-free VEM are used. In this paper we prove that for elliptic self-adjoint eigenvalue problems the stabilization of the mass matrix is not necessary when lower order standard VEM spaces are adopted. Numerical evidence shows that also for higher order schemes the same result is true on various mesh sequences.
Cite
@article{arxiv.2604.03751,
title = {Virtual element approximation of eigenvalue problems: is the stabilization of the right hand side necessary?},
author = {Daniele Boffi and Francesca Gardini and Lucia Gastaldi},
journal= {arXiv preprint arXiv:2604.03751},
year = {2026}
}