H. Li was partially supported by the NSF Grant DMS-1158839. J.S. Ovall was partially supported by the NSF Grant DMS-1216672.
Eigenvalues, Schrödinger operator, Finite elements, Estimation (Mathematics)
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.
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.