Numerical analysis on the mortar spectral element methods for Schrödinger eigenvalue problem with an inverse square potential

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 squar...

Full description

Saved in:
Bibliographic Details
Published in:Applied numerical mathematics 2020-12, Vol.158, p.54-84
Main Authors: Jia, Lueling, Li, Huiyuan, Zhang, Zhimin
Format: Article
Language:English
Subjects:
hp Error estimate
Mortar spectral element method
Regularity analysis
Schrödinger eigenvalue problem
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:0168-9274
1873-5460
DOI:10.1016/j.apnum.2020.06.015