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

DOI10.3934/dcdsb.2015.20.1377zbMath1334.65190OpenAlexW1218236336MaRDI QIDQ256826

Jeffrey S. Ovall, Hengguang Li

Publication date: 10 March 2016

Published in: Discrete and Continuous Dynamical Systems. Series B (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcdsb.2015.20.1377

zbMATH Keywords

finite elementsSchrödinger operatorerror estimationeigenvalue problemsnumerical experimentasymptotic exactness

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) Error bounds for boundary value problems involving PDEs (65N15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Schrödinger operator, Schrödinger equation (35J10) Numerical methods for eigenvalue problems for boundary value problems involving PDEs (65N25)

Related Items (5)

An efficient finite element method and error analysis for eigenvalue problem of Schrödinger equation with an inverse square potential on spherical domain ⋮ Novel spectral methods for Schrödinger equations with an inverse square potential on the whole space ⋮ Efficient Spectral and Spectral Element Methods for Eigenvalue Problems of Schrödinger Equations with an Inverse Square Potential ⋮ An overview of \textit{a posteriori} error estimation and post-processing methods for nonlinear eigenvalue problems ⋮ Numerical analysis on the mortar spectral element methods for Schrödinger eigenvalue problem with an inverse square potential

Uses Software

• PLTMG
• ARPACK

Cites Work

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• A posteriori error estimation of hierarchical type for the Schrödinger operator with inverse square potential
• Asymptotic behavior of solutions to Schrödinger equations near an isolated singularity of the electromagnetic potential
• Analysis of the finite element method for transmission/mixed boundary value problems on general polygonal domains
• Finite element approximations of nonlinear eigenvalue problems in quantum physics
• Nonrelativistic inverse square potential, scale anomaly, and complex extension
• On the behavior of solutions to Schrödinger equations with dipole type potentials near the singularity
• Direct and inverse error estimates for finite elements with mesh refinements
• Elliptic boundary value problems on corner domains. Smoothness and asymptotics of solutions
• Theory and practice of finite elements.
• A framework for robust eigenvalue and eigenvector error estimation and Ritz value convergence enhancement
• Analysis of a modified Schrödinger operator in 2D: Regularity, index, and FEM
• Improving the rate of convergence of `high order finite elements' on polygons and domains with cusps
• Function Value Recovery and Its Application in Eigenvalue Problems
• Analytic structure of solutions to multiconfiguration equations
• ARPACK Users' Guide
• Analysis of Schr\"odinger operators with inverse square potentials I: regularity results in 3D

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