Unconditionally optimal error estimate of mass- and energy-stable Galerkin method for Schrödinger equation with cubic nonlinearity
DOI10.1016/j.apnum.2022.08.016zbMath1500.65074OpenAlexW4293386420WikidataQ113880024 ScholiaQ113880024MaRDI QIDQ2085677
Publication date: 18 October 2022
Published in: Applied Numerical Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.apnum.2022.08.016
cubic Schrödinger equationbackward Euler schemeunconditionally optimal error estimatemodified Crank-Nicolson scheme
Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) NLS equations (nonlinear Schrödinger equations) (35Q55) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Time-dependent Schrödinger equations and Dirac equations (35Q41)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Computational methods for the dynamics of the nonlinear Schrödinger/Gross-Pitaevskii equations
- A new error analysis of Crank-Nicolson Galerkin FEMs for a generalized nonlinear Schrödinger equation
- Optimal error analysis of Crank-Nicolson schemes for a coupled nonlinear Schrödinger system in 3D
- On the \(L_\infty \) convergence of a difference scheme for coupled nonlinear Schrödinger equations
- Mass preserving discontinuous Galerkin methods for Schrödinger equations
- Error estimates of \(H^1\)-Galerkin mixed finite element method for Schrödinger equation
- Numerical solution of coupled nonlinear Schrödinger equation by Galerkin method
- Analysis of finite element method for one-dimensional time-dependent Schrödinger equation on unbounded domain
- Convergence of a finite element scheme for the two-dimensional time-dependent Schrödinger equation in a long strip
- On fully discrete Galerkin methods of second-order temporal accuracy for the nonlinear Schrödinger equation
- Difference schemes for solving the generalized nonlinear Schrödinger equation
- Error analysis of mixed finite element methods for nonlinear parabolic equations
- Unconditional stability and convergence of Crank-Nicolson Galerkin FEMs for a nonlinear Schrödinger-Helmholtz system
- Local discontinuous Galerkin methods for nonlinear Schrödinger equations
- Superconvergence analysis of finite element method for the time-dependent Schrödinger equation
- Superconvergence error estimate of a linearized energy-stable Galerkin scheme for semilinear wave equation
- Superconvergence error estimate of Galerkin method for Sobolev equation with Burgers' type nonlinearity
- Optimal convergence of the Newton iterative Crank-Nicolson finite element method for the nonlinear Schrödinger equation
- A fully discrete low-regularity integrator for the 1D periodic cubic nonlinear Schrödinger equation
- Unconditionally optimal error estimates of a new mixed FEM for nonlinear Schrödinger equations
- Superconvergence analysis of anisotropic linear triangular finite element for nonlinear Schrödinger equation
- Unconditional superconvergence analysis of a Crank-Nicolson Galerkin FEM for nonlinear Schrödinger equation
- On convergence and stability of a numerical scheme of coupled nonlinear Schrödinger equations
- Analysis of a leap-frog pseudospectral scheme for the Schrödinger equation
- On the convergence of a linear two-step finite element method for the nonlinear Schrödinger equation
- Unconditional Convergence and Optimal Error Estimates of a Galerkin-Mixed FEM for Incompressible Miscible Flow in Porous Media
- Error analysis of linearized semi-implicit Galerkin finite element methods for nonlinear parabolic equations
- A modified numerical scheme for the cubic Schrödinger equation
- Error Estimate of Fourth-Order Compact Scheme for Linear Schrödinger Equations
- Fully Discrete Galerkin Finite Element Method for the Cubic Nonlinear Schrödinger Equation
- A Two-Grid Finite-Element Method for the Nonlinear Schrödinger Equation
- Numerical solution of nonlinear Schrödinger equation by using time-space pseudo-spectral method
- Nonlinear Schrödinger evolution equations
- Optimal H1 Estimates for two Time-discrete Galerkin Approximations of a Nonlinear Schrödinger Equation
- Finite difference discretization of the cubic Schrödinger equation
- A Space-Time Finite Element Method for the Nonlinear Schrödinger Equation: The Continuous Galerkin Method
- Discrete-time Orthogonal Spline Collocation Methods for Schrödinger Equations in Two Space Variables
- High-order Mass- and Energy-conserving SAV-Gauss Collocation Finite Element Methods for the Nonlinear Schrödinger Equation
- Superconvergence analysis of a new linearized MFEM for nonlinear Schrödinger equation
- Mass- and Energy-Conserved Numerical Schemes for Nonlinear Schr ¨odinger Equations
- A New Error Analysis of Characteristics-Mixed FEMs for Miscible Displacement in Porous Media
- Crank-Nicolson finite element discretizations for a two-dimensional linear Schrödinger-type equation posed in a noncylindrical domain
- Conservative compact difference schemes for the coupled nonlinear schrödinger system
- Galerkin Finite Element Methods for Parabolic Problems
- Convergence of Renormalized Finite Element Methods for Heat Flow of Harmonic Maps
This page was built for publication: Unconditionally optimal error estimate of mass- and energy-stable Galerkin method for Schrödinger equation with cubic nonlinearity
