Unconditionally optimal error estimate of mass- and energy-stable Galerkin method for Schrödinger equation with cubic nonlinearity
type: Item
instance of: scholarly article
title: Unconditionally optimal error estimate of mass- and energy-stable Galerkin method for Schrödinger equation with cubic nonlinearity
zbMATH Open document ID: 1500.65074
author: Huaijun Yang
published in: Applied Numerical Mathematics
publication date: 2022-10-18T00:00:00Z
Mathematics Subject Classification ID: 65M60
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 65M15
Mathematics Subject Classification ID: 35Q55
Mathematics Subject Classification ID: 35Q41
zbMATH DE Number: 7603728
zbMATH Keywords: cubic Schrödinger equation
zbMATH Keywords: backward Euler scheme
zbMATH Keywords: modified Crank-Nicolson scheme
zbMATH Keywords: unconditionally optimal error estimate
MaRDI profile type: Publication
full work available at URL: j.apnum.2022.08.016
OpenAlex ID: W4293386420
Wikidata QID: Q113880024
cites work: Q5318420
cites work: Finite difference discretization of the cubic Schrödinger equation
cites work: On fully discrete Galerkin methods of second-order temporal accuracy for the nonlinear Schrödinger equation
cites work: Computational methods for the dynamics of the nonlinear Schrödinger/Gross-Pitaevskii equations
cites work: Crank-Nicolson finite element discretizations for a two-dimensional linear Schrödinger-type equation posed in a noncylindrical domain
cites work: Analysis of a leap-frog pseudospectral scheme for the Schrödinger equation
cites work: A modified numerical scheme for the cubic Schrödinger equation
cites work: Q4531674
cites work: Nonlinear Schrödinger evolution equations
cites work: Difference schemes for solving the generalized nonlinear Schrödinger equation
cites work: Numerical solution of nonlinear Schrödinger equation by using time-space pseudo-spectral method
cites work: Mass- and Energy-Conserved Numerical Schemes for Nonlinear Schr ¨odinger Equations
cites work: High-order Mass- and Energy-conserving SAV-Gauss Collocation Finite Element Methods for the Nonlinear Schrödinger Equation
cites work: Error analysis of mixed finite element methods for nonlinear parabolic equations
cites work: Q3609579
cites work: Convergence of Renormalized Finite Element Methods for Heat Flow of Harmonic Maps
cites work: Optimal convergence of the Newton iterative Crank-Nicolson finite element method for the nonlinear Schrödinger equation
cites work: Conservative compact difference schemes for the coupled nonlinear schrödinger system
cites work: Numerical solution of coupled nonlinear Schrödinger equation by Galerkin method
cites work: Analysis of finite element method for one-dimensional time-dependent Schrödinger equation on unbounded domain
cites work: Convergence of a finite element scheme for the two-dimensional time-dependent Schrödinger equation in a long strip
cites work: A Two-Grid Finite-Element Method for the Nonlinear Schrödinger Equation
cites work: A Space-Time Finite Element Method for the Nonlinear Schrödinger Equation: The Continuous Galerkin Method
cites work: Discrete-time Orthogonal Spline Collocation Methods for Schrödinger Equations in Two Space Variables
cites work: Error analysis of linearized semi-implicit Galerkin finite element methods for nonlinear parabolic equations
cites work: Unconditional convergence and optimal error estimates of a Galerkin-mixed FEM for incompressible miscible flow in porous media
cites work: A fully discrete low-regularity integrator for the 1D periodic cubic nonlinear Schrödinger equation
cites work: Error Estimate of Fourth-Order Compact Scheme for Linear Schrödinger Equations
cites work: Q4236747
cites work: Error estimates of \(H^1\)-Galerkin mixed finite element method for Schrödinger equation
cites work: Mass preserving discontinuous Galerkin methods for Schrödinger equations
cites work: On convergence and stability of a numerical scheme of coupled nonlinear Schrödinger equations
cites work: Unconditional superconvergence analysis of a Crank-Nicolson Galerkin FEM for nonlinear Schrödinger equation
cites work: Unconditionally optimal error estimates of a new mixed FEM for nonlinear Schrödinger equations
cites work: Superconvergence analysis of a new linearized MFEM for nonlinear Schrödinger equation
cites work: Superconvergence analysis of anisotropic linear triangular finite element for nonlinear Schrödinger equation
cites work: Optimal error analysis of Crank-Nicolson schemes for a coupled nonlinear Schrödinger system in 3D
cites work: On the \(L_\infty \) convergence of a difference scheme for coupled nonlinear Schrödinger equations
cites work: Galerkin Finite Element Methods for Parabolic Problems
cites work: Optimal H1 Estimates for two Time-discrete Galerkin Approximations of a Nonlinear Schrödinger Equation
cites work: A new error analysis of Crank-Nicolson Galerkin FEMs for a generalized nonlinear Schrödinger equation
cites work: Fully Discrete Galerkin Finite Element Method for the Cubic Nonlinear Schrödinger Equation
cites work: Superconvergence analysis of finite element method for the time-dependent Schrödinger equation
cites work: Unconditional stability and convergence of Crank-Nicolson Galerkin FEMs for a nonlinear Schrödinger-Helmholtz system
cites work: A New Error Analysis of Characteristics-Mixed FEMs for Miscible Displacement in Porous Media
cites work: Local discontinuous Galerkin methods for nonlinear Schrödinger equations
cites work: Superconvergence error estimate of a linearized energy-stable Galerkin scheme for semilinear wave equation
cites work: Superconvergence error estimate of Galerkin method for Sobolev equation with Burgers' type nonlinearity
cites work: On the convergence of a linear two-step finite element method for the nonlinear Schrödinger equation
DOI: 10.1016/J.APNUM.2022.08.016
description: scientific article; zbMATH DE number 7603728