Abstract
In this paper, we present an hp analysis of the mortar spectral element method for the Schrödinger eigenvalue problem (−Δ+c2‖x‖2)u=λu, and thereby justify the numerical findings in [30], where the method was demonstrated to be efficient to handle the singularities arising from both the inverse square potential and the reentrant/obtuse corners with exponential order of convergence. Non-uniformly weighted Sobolev spaces are introduced to accommodate singularities and to measure the regularity of the eigenfunctions. Optimal error estimates for the mortar spectral element method and the lifting theorem for the eigenfunctions are established.
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