Virtual element approximation of eigenvalue problems: is the stabilization of the right hand side necessary?

Daniele Boffi; Francesca Gardini; Lucia Gastaldi

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arXiv · 2604.03751

Virtual element approximation of eigenvalue problems: is the stabilization of the right hand side necessary?

Daniele Boffi·Francesca Gardini·Lucia Gastaldi

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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.

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Daniele Boffi, Francesca Gardini, Lucia Gastaldi. 2026-04-04. Virtual element approximation of eigenvalue problems: is the stabilization of the right hand side necessary?. https://arxiv.org/abs/2604.03751

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