Sponsor
H. Li was partially supported by the NSF Grant DMS-1158839. J.S. Ovall was partially supported by the NSF Grant DMS-1216672.
Document Type
Post-Print
Publication Date
7-2015
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.
DOI
10.3934/dcdsb.2015.20.1377
Persistent Identifier
http://archives.pdx.edu/ds/psu/15908
Citation Details
Li, Hengguang and Ovall, Jeffrey S., "A Posteriori Eigenvalue Error Estimation for the Schrödinger Operator with the Inverse Square Potential" (2015). Mathematics and Statistics Faculty Publications and Presentations. 109.
http://archives.pdx.edu/ds/psu/15908
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.