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Title: Analysis of Schrodinger operators with inverse square potentials II: FEM and approximation of eigenfunctions in the periodic case
Authors: Hunsicker, Eugenie
Li, Hengguang
Nistor, Victor
Uski, Ville
Keywords: 3D Schrodinger operator
Finite element method
Graded mesh
Issue Date: 2014
Publisher: © Wiley Periodicals, Inc.
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.
Abstract: 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.
Description: 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.
Sponsor: 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
Version: Accepted for publication
DOI: 10.1002/num.21861
URI: https://dspace.lboro.ac.uk/2134/17169
Publisher Link: http://dx.doi.org/10.1002/num.21861
ISSN: 0749-159X
Appears in Collections:Published Articles (Maths)

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