Approximation of PDE eigenvalue problems involving parameter dependent matrices

Abstract

We discuss the solution of eigenvalue problems associated with partial differential equations that can be written in the generalized form Ax = λBx, where the matrices A and/or B may depend on a scalar parameter. We consider in particular the approximation of Poisson eigenvalue problem using the Virtual Element Method (VEM) and show that the presence of one (or both) parameters can produce unexpected results.