Cardiff University | Prifysgol Caerdydd ORCA
Online Research @ Cardiff 
WelshClear Cookie - decide language by browser settings

Neumann-Dirichlet maps and analysis of spectral pollution for non-self-adjoint elliptic PDEs with real essential spectrum

Marletta, Marco 2010. Neumann-Dirichlet maps and analysis of spectral pollution for non-self-adjoint elliptic PDEs with real essential spectrum. IMA Journal of Numerical Analysis 30 (4) , pp. 917-939. 10.1093/imanum/drp017

Full text not available from this repository.

Abstract

We prove that one of the most commonly used techniques for approximating the spectra of certain classes of non-self-adjoint elliptic partial differential equations on exterior domains does not suffer from spectral pollution except possibly in the spectral gaps. This generalizes a well-known result from the self-adjoint case. We also show how the method can be used in conjunction with some simple tricks to avoid spectral pollution for the self-adjoint case. Our proofs are based on a new approach to the nesting set analysis for Neumann to Dirichlet maps first proposed by Amrein and Pearson in 2004, with enhanced convergence results obtained from an elliptic regularity bootstrapping procedure. The numerical results in Section 6 illustrate a technique for finding eigenvalues in spectral gaps of self-adjoint operators by means of a compactly supported complex shift. This method seems to be of independent interest and can be understood without reading the rest of the paper.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Mathematics
Subjects: Q Science > QA Mathematics
Uncontrolled Keywords: boundary-value problem; eigenvalue problem; essential spectrum; Neumann to Dirichlet map; Schrödinger equation; spectral pollution; Sturm–Liouville problem
Publisher: Oxford University Press
ISSN: 0272-4979
Funders: EPSRC
Last Modified: 04 Feb 2019 00:01
URI: http://orca.cf.ac.uk/id/eprint/10968

Citation Data

Cited 10 times in Google Scholar. View in Google Scholar

Cited 14 times in Scopus. View in Scopus. Powered By Scopus® Data

Actions (repository staff only)

Edit Item Edit Item