  In this paper we present benchmark problems for non-selfadjoint elliptic
eigenvalue problems with large defect and ascent. We describe the derivation of
the benchmark problem with a discontinuous coefficient and mixed boundary
conditions. Numerical experiments are performed to investigate the convergence
of a Galerkin finite element method with respect to the discretization
parameters, the regularity of the problem, and the ascent of the eigenvalue.
This allows us to verify the sharpness of the theoretical estimates from the
literature with respect to these parameters. We provide numerical evidence
about the size of the ascent and show that it is important to consider the mean
value for the eigenvalue approximation.
