Unconditionally superconvergence error analysis of an energy-stable finite element method for Schrödinger equation with cubic nonlinearity
DOI10.1016/j.cnsns.2024.108383MaRDI QIDQ6649272
Huaijun Yang, Jinjin Yang, Xu Jia
Publication date: 5 December 2024
Published in: Communications in Nonlinear Science and Numerical Simulation (Search for Journal in Brave)
cubic Schrödinger equationenergy-stable finite element methodunconditionally superclose and superconvergence error estimates
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) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Numerical interpolation (65D05) 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
- 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
- Mass preserving discontinuous Galerkin methods for Schrödinger equations
- Simple finite element numerical simulation of incompressible flow over non-rectangular domains and the super-convergence analysis
- 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 optimal error estimates for BDF2-FEM for a nonlinear Schrödinger equation
- The finite difference scheme for nonlinear Schrödinger equations on unbounded domain by artificial boundary conditions
- Unconditionally optimal error estimate of mass- and energy-stable Galerkin method for Schrödinger equation with cubic nonlinearity
- Error estimates of second-order BDF Galerkin finite element methods for a coupled nonlinear Schrödinger system
- 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 convergence and optimal error estimates of the Euler semi-implicit scheme for a generalized nonlinear Schrödinger equation
- Unconditional superconvergence analysis of a Crank-Nicolson Galerkin FEM for nonlinear Schrödinger equation
- An ultra-weak discontinuous Galerkin method for Schrödinger equation in one dimension
- A note on optimal \(H^1\)-error estimates for Crank-Nicolson approximations to 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
- Optimal H1 Estimates for two Time-discrete Galerkin Approximations of a Nonlinear Schrödinger Equation
- Finite difference discretization of the cubic Schrödinger equation
- Unconditional superconvergence analysis of a linearized Galerkin FEM for nonlinear Schrödinger equation
- Superconvergence analysis of a new linearized MFEM for nonlinear Schrödinger equation
- A Space-Time Trefftz Discontinuous Galerkin Method for the Linear Schrödinger Equation
- Optimal Error Estimates of a Linearized Crank-Nicolson Galerkin FEM for the Kuramoto-Tsuzuki Equations
- Mass- and Energy-Conserved Numerical Schemes for Nonlinear Schr ¨odinger Equations
- Conservative compact difference schemes for the coupled nonlinear schrödinger system
- Galerkin Finite Element Methods for Parabolic Problems
- Unconditionally optimal error estimate of the Crank-Nicolson extrapolation Galerkin finite element method for Kuramoto-Tsuzuki equation
- Convergence and superconvergence analysis of energy-preserving Crank–Nicolson Galerkin method for the Benjamin–Bona–Mahony equation
This page was built for publication: Unconditionally superconvergence error analysis of an energy-stable finite element method for Schrödinger equation with cubic nonlinearity
