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

Eugénie Hunsicker, Hengguang Li, Victor Nistor, Ville Uski

Research output: Contribution to journalArticle

1 Citation (Scopus)

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 alternative 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.

Original languageEnglish (US)
Pages (from-to)1130-1151
Number of pages22
JournalNumerical Methods for Partial Differential Equations
Volume30
Issue number4
DOIs
StatePublished - Jul 2014

Fingerprint

Optimal Approximation
Eigenvalues and eigenfunctions
Eigenfunctions
Mathematical operators
Finite Element Method
Mesh
Graded Meshes
Finite element method
Approximation
Operator
Alternatives
Class
Standards

All Science Journal Classification (ASJC) codes

  • Analysis
  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

Cite this

@article{c4368735577e40838508e929219c77f7,
title = "Analysis of Schr{\"o}dinger operators with inverse square potentials II: FEM and approximation of eigenfunctions in the periodic case",
abstract = "In this article, we consider the problem of optimal approximation of eigenfunctions of Schr{\"o}dinger 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 alternative 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.",
author = "Eug{\'e}nie Hunsicker and Hengguang Li and Victor Nistor and Ville Uski",
year = "2014",
month = "7",
doi = "10.1002/num.21861",
language = "English (US)",
volume = "30",
pages = "1130--1151",
journal = "Numerical Methods for Partial Differential Equations",
issn = "0749-159X",
publisher = "John Wiley and Sons Inc.",
number = "4",

}

Analysis of Schrödinger operators with inverse square potentials II : FEM and approximation of eigenfunctions in the periodic case. / Hunsicker, Eugénie; Li, Hengguang; Nistor, Victor; Uski, Ville.

In: Numerical Methods for Partial Differential Equations, Vol. 30, No. 4, 07.2014, p. 1130-1151.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Analysis of Schrödinger operators with inverse square potentials II

T2 - FEM and approximation of eigenfunctions in the periodic case

AU - Hunsicker, Eugénie

AU - Li, Hengguang

AU - Nistor, Victor

AU - Uski, Ville

PY - 2014/7

Y1 - 2014/7

N2 - 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 alternative 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.

AB - 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 alternative 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.

UR - http://www.scopus.com/inward/record.url?scp=84899511547&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84899511547&partnerID=8YFLogxK

U2 - 10.1002/num.21861

DO - 10.1002/num.21861

M3 - Article

AN - SCOPUS:84899511547

VL - 30

SP - 1130

EP - 1151

JO - Numerical Methods for Partial Differential Equations

JF - Numerical Methods for Partial Differential Equations

SN - 0749-159X

IS - 4

ER -