Unconditional error estimates of linearized BDF2-Galerkin FEMs for nonlinear coupled Schrödinger-Helmholtz equations

DOI10.1007/s11075-022-01360-5OpenAlexW4289856104MaRDI QIDQ2699993

Houchao Zhang, Dong-Yang Shi

Publication date: 20 April 2023

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11075-022-01360-5

zbMATH Keywords

optimal error estimatesGalerkin FEMsSchrödinger-Helmholtz equationslinearized BDF2 scheme

Mathematics Subject Classification ID

Error bounds for boundary value problems involving PDEs (65N15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unconditional optimal error estimates of BDF-Galerkin FEMs for nonlinear thermistor equations
• A new error analysis of Crank-Nicolson Galerkin FEMs for a generalized nonlinear Schrödinger equation
• Finite volume methods for a Keller-Segel system: discrete energy, error estimates and numerical blow-up analysis
• Optimal error analysis of Crank-Nicolson schemes for a coupled nonlinear Schrödinger system in 3D
• On the computation of ground state and dynamics of Schrödinger-Poisson-Slater system
• Unconditional superconvergence analysis of a new mixed finite element method for nonlinear Sobolev equation
• Analysis of the second-order BDF scheme with variable steps for the molecular beam epitaxial model without slope selection
• Spectral method for solving the system of equations of Schrödinger- Klein-Gordon field
• The Schrödinger-Poisson-\(X\alpha\) equation
• Unconditional and optimal \(H^2\)-error estimates of two linear and conservative finite difference schemes for the Klein-Gordon-Schrödinger equation in high dimensions
• Unconditional stability and convergence of Crank-Nicolson Galerkin FEMs for a nonlinear Schrödinger-Helmholtz system
• Unconditionally optimal error analysis of Crank-Nicolson Galerkin FEMs for a strongly nonlinear parabolic system
• Convergence of a conservative difference scheme for a class of Klein-Gordon-Schrödinger equations in one space dimension
• Optimal error estimate of a linear Fourier pseudo-spectral scheme for two dimensional Klein-Gordon-Schrödinger equations
• Point-wise errors of two conservative difference schemes for the Klein-Gordon-Schrödinger equation
• Multisymplectic Fourier pseudo-spectral integrators for Klein-Gordon-Schrödinger equations
• Nonconforming finite element method for a generalized nonlinear Schrödinger equation
• Structure-preserving algorithms for the two-dimensional fractional Klein-Gordon-Schrödinger equation
• Superconvergence analysis of two-grid methods for bacteria equations
• Unconditional superconvergence analysis of the conservative linearized Galerkin FEMs for nonlinear Klein-Gordon-Schrödinger equation
• 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
• A linearized energy-conservative finite element method for the nonlinear Schrödinger equation with wave operator
• Effective one particle quantum dynamics of electrons: a numerical study of the Schrödinger-Poisson-X\(_\alpha\) model
• Unconditional optimal error estimates of linearized backward Euler Galerkin FEMs for nonlinear Schrödinger-Helmholtz equations
• 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
• Uniform Error Estimates of Finite Difference Methods for the Nonlinear Schrödinger Equation with Wave Operator
• A modified numerical scheme for the cubic Schrödinger equation
• On splitting methods for Schrödinger-Poisson and cubic nonlinear Schrödinger equations
• Error Estimate of Fourth-Order Compact Scheme for Linear Schrödinger Equations
• Absorbing Boundary Conditions for General Nonlinear Schrödinger Equations
• Energy Solution to a Schrödinger–Poisson System in the Two-Dimensional Whole Space
• Nonlinear Schrödinger–Helmholtz equation as numerical regularization of the nonlinear Schrödinger equation
• Well posedness and smoothing effect of Schrödinger-Poisson equation
• Superconvergence analysis of Crank‐Nicolson Galerkin FEMs for a generalized nonlinear Schrödinger equation
• Stability and convergence of a second-order mixed finite element method for the Cahn–Hilliard equation
• A numerical study of the Schr dinger Newton equations
• On Energy Stable, Maximum-Principle Preserving, Second-Order BDF Scheme with Variable Steps for the Allen--Cahn Equation
• Unconditionally Optimal Error Estimates of a Crank--Nicolson Galerkin Method for the Nonlinear Thermistor Equations
• Error Estimates for Galerkin Approximations to the Periodic Schrödinger‐Poisson System
• THE IVP FOR THE SCHRÖDINGER–POISSON-Xα EQUATION IN ONE DIMENSION

This page was built for publication: Unconditional error estimates of linearized BDF2-Galerkin FEMs for nonlinear coupled Schrödinger-Helmholtz equations