# American Institute of Mathematical Sciences

July  2015, 20(5): 1377-1391. doi: 10.3934/dcdsb.2015.20.1377

## A posteriori eigenvalue error estimation for a Schrödinger operator with inverse square potential

 1 Department of Mathematics, Wayne State University, Detroit, MI 48202, United States 2 Fariborz Maseeh Department of Mathematics & Statistics, Portland State University, Portland, OR 97201, United States

Received  August 2013 Revised  January 2015 Published  May 2015

We develop an a posteriori error estimate of hierarchical type for Dirichlet eigenvalue problems of the form $(-\Delta+(c/r)^2)\psi=\lambda \psi$ on bounded domains $\Omega$, where $r$ is the distance to the origin, which is assumed to be in $\overline\Omega$. 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.
Citation: Hengguang Li, Jeffrey S. Ovall. A posteriori eigenvalue error estimation for a Schrödinger operator with inverse square potential. Discrete & Continuous Dynamical Systems - B, 2015, 20 (5) : 1377-1391. doi: 10.3934/dcdsb.2015.20.1377
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