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

Hengguang Li; Jeffrey S. Ovall

doi:10.3934/dcdsb.2015.20.1377

Article Contents

2015, Volume 20, Issue 5: 1377-1391. Doi: 10.3934/dcdsb.2015.20.1377

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

Hengguang Li^1, and
Jeffrey S. Ovall^2,

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

Received: August 2013

Revised: January 2015

Published: July 2015

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Abstract

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.

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

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