A perturbation-method-based a posteriori estimator for the planewave discretization of nonlinear Schrödinger equations

DOI10.1016/j.crma.2014.09.014zbMath1303.65077OpenAlexW2077602404WikidataQ60146771 ScholiaQ60146771MaRDI QIDQ470142

Benjamin Stamm, Martin Vohralík, Geneviève Dusson, Yvon Maday, Eric Cancès

Publication date: 11 November 2014

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.crma.2014.09.014

zbMATH Keywords

convergenceperturbation theorynumerical examplesGross-Pitaevskii equationFourier methodperiodic Schrödinger operatorsa posteriori estimator

Mathematics Subject Classification ID

Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Series solutions to PDEs (35C10) NLS equations (nonlinear Schrödinger equations) (35Q55) PDEs in connection with quantum mechanics (35Q40) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15)

Related Items (10)

Guaranteed and robust a posteriori bounds for Laplace eigenvalues and eigenvectors: a unified framework ⋮ Analysis of the Feshbach–Schur method for the Fourier spectral discretizations of Schrödinger operators ⋮ Gradient flow finite element discretizations with energy-based adaptivity for the Gross-Pitaevskii equation ⋮ An overview of \textit{a posteriori} error estimation and post-processing methods for nonlinear eigenvalue problems ⋮ An efficient adaptive mesh redistribution method for nonlinear eigenvalue problems in Bose-Einstein condensates ⋮ Guaranteed and Robust a Posteriori Bounds for Laplace Eigenvalues and Eigenvectors: Conforming Approximations ⋮ Mathematical methods in quantum chemistry. Abstracts from the workshop held March 18--24, 2018 ⋮ The \(J\)-method for the Gross-Pitaevskii eigenvalue problem ⋮ Computable error estimates for ground state solution of Bose-Einstein condensates ⋮ An Adaptive Planewave Method for Electronic Structure Calculations

Cites Work

• Numerical analysis of nonlinear eigenvalue problems
• Adaptive error control for multigrid finite element methods
• A posteriori estimation of the linearization error for strongly monotone nonlinear operators
• Adaptive Inexact Newton Methods with A Posteriori Stopping Criteria for Nonlinear Diffusion PDEs

This page was built for publication: A perturbation-method-based a posteriori estimator for the planewave discretization of nonlinear Schrödinger equations