Benchmark computation of eigenvalues with large defect for non-selfadjoint elliptic differential operators
Numerical Analysis
2019-09-13 v2 Numerical Analysis
Abstract
In this paper we present benchmark problems for non-selfadjoint elliptic eigenvalue problems with large defect and ascent. We describe the derivation of the benchmark problem with a discontinuous coefficient and mixed boundary conditions. Numerical experiments are performed to investigate the convergence of a Galerkin finite element method with respect to the discretization parameters, the regularity of the problem, and the ascent of the eigenvalue. This allows us to verify the sharpness of the theoretical estimates from the literature with respect to these parameters. We provide numerical evidence about the size of the ascent and show that it is important to consider the mean value for the eigenvalue approximation.
Cite
@article{arxiv.1902.02114,
title = {Benchmark computation of eigenvalues with large defect for non-selfadjoint elliptic differential operators},
author = {Rebekka Gasser and Joscha Gedicke and Stefan Sauter},
journal= {arXiv preprint arXiv:1902.02114},
year = {2019}
}