Approximation of PDE eigenvalue problems involving parameter dependent matrices

We discuss the solution of eigenvalue problems associated with partial differential equations that can be written in the generalized form $${\mathsf {A}}x=\lambda {\mathsf {B}}x$$ A x = λ B x , where the matrices $${\mathsf {A}}$$ A and/or $${\mathsf {B}}$$ B may depend on a scalar parameter. Parameter dependent matrices occur frequently when stabilized formulations are used for the numerical approximation of partial differential equations. With the help of classical numerical examples we show that the presence of one (or both) parameters can produce unexpected results.