Virtual element approximation of eigenvalue problems: is the stabilization of the right hand side necessary?
Simplifies the VEM approach for eigenvalue problems by eliminating the need for mass matrix stabilization, benefiting researchers and practitioners using virtual element methods.
The paper proves that for elliptic self-adjoint eigenvalue problems, stabilization of the mass matrix is unnecessary when using lower-order standard VEM spaces, with numerical evidence extending to higher-order schemes on various meshes.
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.