  We consider a general framework for investigating spectral pollution in the
Galerkin method. We show how this phenomenon is characterised via the existence
of particular Weyl sequences which are singular in a suitable sense. For a
semi-bounded selfadjoint operator A we identify relative compactness conditions
on a selfadjoint perturbation B ensuring that the limiting set of spectral
pollution of A and B coincide. Our results show that, under perturbation, this
limiting set behaves in a similar fashion as the essential spectrum.
