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Article
A Posteriori Eigenvalue Error Estimation for the Schrödinger Operator with the Inverse Square Potential
Mathematics and Statistics Faculty Publications and Presentations
  • Hengguang Li, Wayne State University
  • Jeffrey S. Ovall, Portland State University
Document Type
Post-Print
Publication Date
7-1-2015
Subjects
  • Eigenvalues,
  • Schrödinger operator,
  • Finite elements,
  • Estimation (Mathematics)
Abstract
We develop an a posteriori error estimate of hierarchical type for Dirichlet eigenvalue problems of the form (−∆ + (c/r) 2 )ψ = λψ on bounded domains Ω, where r is the distance to the origin, which is assumed to be in Ω. This error estimate is proven to be asymptotically identical to the eigenvalue approximation error on a family of geometrically-graded meshes. Numerical experiments demonstrate this asymptotic exactness in practice.
Description

This is a pre-copy-editing, author-produced PDF of an article accepted for publication by the American Institute of Mathematical Sciences in Discrete and Continuous Dynamical Systems - Series B following peer review. The definitive publisher-authenticated version is available online at the publisher's site.

DOI
10.3934/dcdsb.2015.20.1377
Persistent Identifier
http://archives.pdx.edu/ds/psu/15908
Citation Information
Hengguang Li and Jeffrey S. Ovall. "A Posteriori Eigenvalue Error Estimation for the Schrödinger Operator with the Inverse Square Potential" (2015)
Available at: http://works.bepress.com/jeffrey_ovall/3/