Premium
Analysis of Schrödinger operators with inverse square potentials II: FEM and approximation of eigenfunctions in the periodic case
Author(s) -
Hunsicker Eugénie,
Li Hengguang,
Nistor Victor,
Uski Ville
Publication year - 2014
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.21861
Subject(s) - eigenfunction , mathematics , polygon mesh , finite element method , inverse , square (algebra) , inverse problem , differential operator , class (philosophy) , mathematical analysis , eigenvalues and eigenvectors , geometry , computer science , physics , quantum mechanics , thermodynamics , artificial intelligence
In this article, we consider the problem of optimal approximation of eigenfunctions of Schrödinger operators with isolated inverse square potentials and of solutions to equations involving such operators. It is known in this situation that the finite element method performs poorly with standard meshes. We construct an alternative class of graded meshes, and prove and numerically test optimal approximation results for the finite element method using these meshes. Our numerical tests are in good agreement with our theoretical results.Copyright © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 1130–1151, 2014