Robust Eigenvalue Computation for Smoothing Operators
Radu Alexandru Todor · SIAM Journal on Numerical Analysis · 2006
Robust quasi-relative Galerkin discretization error estimates are derived for the eigenvalue problem associated to a nonnegative compact operator $\cal K$ acting in a Hilbert space. Trace discretization error estimates for arbitrarily small positive powers of $\cal K$ are obtained as a consequence. Coupled with bounds on eigenfunction oscillations, the results are then applied to the case of an integral operator with (piecewise) smooth kernel K on a bounded domain and in the context of the h finite element method.