A posteriori eigenvalue error estimation for a Schrödinger operator with inverse square potential
Hengguang Li Jeffrey S. Ovall
Discrete & Continuous Dynamical Systems - B 2015, 20(5): 1377-1391 doi: 10.3934/dcdsb.2015.20.1377
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.
keywords: error estimation finite elements asymptotic exactness. Schrödinger operator Eigenvalue problems

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