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Robust eigenvalue computation for integral operators with smooth kernel

by R. A. Todor

(Report number 2004-11)

Abstract
Eigenfunction oscillations for a compact integral operator $\cal K$ on a bounded domain are investigated, in terms of the kernel regularity. The results are used to obtain robust quasi-relative Galerkin discretization error estimates for the eigenvalue problem in the case of a nonnegative $\cal K$ with smooth kernel. Both the h (for the smooth kernel) and the p (for the analytic kernel) finite element methods (FEM) are considered. As a consequence, robust trace discretization error estimates for arbitrarily small positive powers of $\cal K$ are derived.

Keywords:

@Techreport{T04_338,
  author = {R. A. Todor},
  title = {Robust eigenvalue computation for integral operators with smooth kernel},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2004-11},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2004/2004-11.pdf },
  year = {2004}
}

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