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Full-Text Articles in Dynamical Systems
A Posteriori Eigenvalue Error Estimation For The Schrödinger Operator With The Inverse Square Potential, Hengguang Li, Jeffrey S. Ovall
A Posteriori Eigenvalue Error Estimation For The Schrödinger Operator With The Inverse Square Potential, Hengguang Li, Jeffrey S. Ovall
Mathematics and Statistics Faculty Publications and Presentations
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.