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

2 Scopus citations

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

All Science Journal Classification (ASJC) codes

  • Analysis
  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

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