  We present a perturbed subspace iteration algorithm to approximate the
lowermost eigenvalue cluster of an elliptic eigenvalue problem. As a prototype,
we consider the Laplace eigenvalue problem posed in a polygonal domain. The
algorithm is motivated by the analysis of inexact (perturbed) inverse iteration
algorithms in numerical linear algebra. We couple the perturbed inverse
iteration approach with mesh refinement strategy based on residual estimators.
We demonstrate our approach on model problems in two and three dimensions.
