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Analysis of Schrodinger operators with inverse square potentials II: FEM and approximation of eigenfunctions in the periodic case

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posted on 01.04.2015, 10:58 authored by Eugenie Hunsicker, Hengguang Li, Victor Nistor, Ville Uski
In this article, we consider the problem of optimal approximation of eigenfunctions of Schrödinger operators with isolated inverse square potentials and of solutions to equations involving such operators. It is known in this situation that the finite element method performs poorly with standard meshes. We construct an alter- native class of graded meshes, and prove and numerically test optimal approximation results for the finite element method using these meshes. Our numerical tests are in good agreement with our theoretical results.

Funding

Contract grant sponsor: Leverhulme Trust (E.H.); contract grant number: J11695 Contract grant sponsor: NSF (H.L.); contract grant number: 1158839 Contract grant sponsor: NSF (V.N.); contract grant numbers: OCI-0749202 and DMS-1016556

History

School

  • Science

Department

  • Mathematical Sciences

Published in

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS

Volume

30

Issue

4

Pages

1130 - 1151 (22)

Citation

HUNSICKER, E. ... et al, 2014. Analysis of Schrodinger operators with inverse square potentials II: FEM and approximation of eigenfunctions in the periodic case. Numerical Methods for Partial Differential Equations, 30 (4), pp. 1130 - 1151.

Publisher

© Wiley Periodicals, Inc.

Version

AM (Accepted Manuscript)

Publisher statement

This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/

Publication date

2014

Notes

This is the peer reviewed version of the following article: HUNSICKER, E. ... et al, 2014. Analysis of Schrodinger operators with inverse square potentials II: FEM and approximation of eigenfunctions in the periodic case. Numerical Methods for Partial Differential Equations, 30 (4), pp. 1130 - 1151, which has been published in final form at http://dx.doi.org/10.1002/num.21861 . This article may be used for non-commercial purposes in accordance With Wiley Terms and Conditions for self-archiving.

ISSN

0749-159X

Language

en