Analysis of Schrödinger operators with inverse square potentials II: FEM and approximation of eigenfunctions in the periodic case. Issue 4 (6th February 2014)

• Record Type: Journal Article
• Authors: Hunsicker, Eugénie; Li, Hengguang; Nistor, Victor; Uski, Ville
• Is Part Of: Numerical methods for partial differential equations. Volume 30:Issue 4(2014:Jul.)
• Page Start: 1130
• Page End: 1151
• Publication Date: 2014-02-06
• Subjects: Differential equations, Partial -- Numerical solutions -- Periodicals; 515.353
• DOI: 10.1002/num.21861
• Languages: English
• ISSNs: 0749-159X

Abstract

<abstract abstract-type="main"> <title>Abstract</title> <p>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.Copyright © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 1130–1151, 2014</p> </abstract>