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

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  • 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.
    Mathematics Subject Classification: Primary: 65N30, 65N25; Secondary: 65N15, 65N50.


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