Regularity and Numerical Solution of Eigenvalue Problems with Piecewise Analytic Data

Abstract

This paper discusses the regularity of the eigenfunctions of eigenvalue problems with piecewise analytic data and the approximation of the eigenvalues and eigenfunctions of such problems. A detailed and systematic numerical study of these approximations is presented, together with an analysis of the numerical results in light of the theoretical results. The specific aim is to assess the reliability of the theoretical results, which are of an asymptotic nature, as a guide to practical computations, which may take place in the pre-asymptotic phase, and to look for characteristic features of the numerical results that are not completely explained by known theoretical results.