Unconditional optimal error estimates of a linearized mass- and energy-conservation FEM for a coupled nonlinear Schrödinger equations

DOI10.1016/j.cnsns.2023.107297MaRDI QIDQ6116814

No author found.

Publication date: 18 July 2023

Published in: Communications in Nonlinear Science and Numerical Simulation (Search for Journal in Brave)

zbMATH Keywords

finite element methodscoupled nonlinear Schrödinger equationsunconditional optimal error estimatesmass- and energy-conservation

Mathematics Subject Classification ID

Numerical analysis (65-XX) Ordinary differential equations (34-XX) Partial differential equations (35-XX) Systems theory; control (93-XX)

Cites Work

• Unnamed Item
• Unnamed Item
• Spectral collocation methods using sine functions for a rotating Bose-Einstein condensation in optical lattices
• The time-splitting Fourier spectral method for the coupled Schrödinger-Boussinesq equations
• A Hamiltonian preserving discontinuous Galerkin method for the generalized Korteweg-de Vries equation
• Convergence of the Lambert-McLeod trajectory solver and of the CELF method
• Local discontinuous Galerkin methods for the generalized Zakharov system
• A linearly implicit conservative scheme for the coupled nonlinear Schrödinger equation
• A method for the integration in time of certain partial differential equations
• An explicit finite-difference scheme with exact conservation properties
• On fully discrete Galerkin methods of second-order temporal accuracy for the nonlinear Schrödinger equation
• Optimal error estimate of conservative local discontinuous Galerkin method for nonlinear Schrödinger equation
• Local discontinuous Galerkin methods for nonlinear Schrödinger equations
• \(B\)-spline finite element studies of the nonlinear Schrödinger equation
• Conservative local discontinuous Galerkin methods for a generalized system of strongly coupled nonlinear Schrödinger equations.
• Error estimates of second-order BDF Galerkin finite element methods for a coupled nonlinear Schrödinger system
• Two novel classes of linear high-order structure-preserving schemes for the generalized nonlinear Schrödinger equation
• Cubic B-spline Galerkin method for numerical solution of the coupled nonlinear Schrödinger equation
• Structure preserving -- field directional splitting difference methods for nonlinear Schrödinger systems
• A unified framework of high order structure-preserving B-splines Galerkin methods for coupled nonlinear Schrödinger systems
• Conservative super-convergent and hybrid discontinuous Galerkin methods applied to nonlinear Schrödinger equations
• A linearized energy-conservative finite element method for the nonlinear Schrödinger equation with wave operator
• Self-similarity and asymptotic stability for coupled nonlinear Schrödinger equations in high dimensions
• The stability and convergence of a difference scheme for the Schrödinger equation on an infinite domain by using artificial boundary conditions
• Analysis of a leap-frog pseudospectral scheme for the Schrödinger equation
• Stability Analysis of Multipulses in Nonlinearly-Coupled Schrodinger Equations
• On the convergence of a linear two-step finite element method for the nonlinear Schrödinger equation
• Conservative, discontinuous Galerkin–methods for the generalized Korteweg–de Vries 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
• Absorbing Boundary Conditions for General Nonlinear Schrödinger Equations
• Methods for the Numerical Solution of the Nonlinear Schroedinger Equation
• An a Posteriori Error Estimate and Adaptive Timestep Control for a Backward Euler Discretization of a Parabolic Problem
• Multilevel Spectral-Galerkin and Continuation Methods for Nonlinear Schrödinger Equations
• Numerical solution of nonlinear Schrödinger equation by using time-space pseudo-spectral method
• Optimal H¹ Estimates for two Time-discrete Galerkin Approximations of a Nonlinear Schrödinger Equation
• Discrete-time Orthogonal Spline Collocation Methods for Schrödinger Equations in Two Space Variables
• Stability of solitary waves for coupled nonlinear schrödinger equations
• Dufort–Frankel-Type Methods for Linear and Nonlinear Schrödinger Equations
• New development in freefem++
• Nonconforming quadrilateral finite element method for nonlinear Kirchhoff‐type equation with damping
• Two Kinds of New Energy-Preserving Schemes for the Coupled Nonlinear Schrödinger Equations
• Linearized FE Approximations to a Nonlinear Gradient Flow
• A New Error Analysis of Characteristics-Mixed FEMs for Miscible Displacement in Porous Media
• Optimal Error Estimates of Linearized Crank-Nicolson Galerkin FEMs for the Time-Dependent Ginzburg--Landau Equations in Superconductivity
• Unconditionally Optimal Error Estimates of a Crank--Nicolson Galerkin Method for the Nonlinear Thermistor Equations
• Numerical simulation of coupled nonlinear Schrödinger equation

This page was built for publication: Unconditional optimal error estimates of a linearized mass- and energy-conservation FEM for a coupled nonlinear Schrödinger equations