Conservative Conforming and Nonconforming Vems for Fourth Order Nonlinear Schrödinger Equations with Trapped Term

DOI10.4208/jcm.2209-m2021-0038MaRDI QIDQ6197990

Jikun Zhao, Zhongchi Wang, Meng Li, Shao-Chun Chen

Publication date: 20 February 2024

Published in: Journal of Computational Mathematics (Search for Journal in Brave)

convergence nonlinear Schrödinger equation conservation $C^0$ nonconforming virtual element $H^2$ conforming virtual element Morley-type nonconforming virtual element

Mathematics Subject Classification ID

Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Error bounds for boundary value problems involving PDEs (65N15) Stokes and related (Oseen, etc.) flows (76D07) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12)

Cites Work

Unnamed Item
Unnamed Item
Equivalent projectors for virtual element methods
Fourth-order compact and energy conservative difference schemes for the nonlinear Schrödinger equation in two dimensions
Virtual element methods for plate bending problems
A new error analysis of Crank-Nicolson Galerkin FEMs for a generalized nonlinear Schrödinger equation
Virtual element method for fourth order problems: $L^2$-estimates
A compact split-step finite difference method for solving the nonlinear Schrödinger equations with constant and variable coefficients
On fully discrete Galerkin methods of second-order temporal accuracy for the nonlinear Schrödinger equation
Difference schemes for solving the generalized nonlinear Schrödinger equation
The nonlinear Schrödinger equation. Self-focusing and wave collapse
A conservative numerical scheme for a class of nonlinear Schrödinger equation with wave operator.
The Morley-type virtual element for plate bending problems
A virtual element method for contact
Some error analysis on virtual element methods
$C^{0}$-nonconforming tetrahedral and cuboid elements for the three-dimensional fourth-order elliptic problem
A medius error analysis for nonconforming virtual element methods for Poisson and biharmonic equations
Conforming and nonconforming conservative virtual element methods for nonlinear Schrödinger equation: a unified framework
Symplectic integrator for nonlinear high order Schrödinger equation with a trapped term
Nonconforming virtual element method for the time fractional reaction-subdiffusion equation with non-smooth data
Some estimates for virtual element methods
The nonconforming virtual element method for elasticity problems
Unconditional superconvergence analysis of a Crank-Nicolson Galerkin FEM for nonlinear Schrödinger equation
Exact solutions for the fourth order nonlinear Schrödinger equations with cubic and power law nonlinearities
The Cauchy problem for the fourth-order nonlinear Schrödinger equation related to the vortex filament
The nonconforming virtual element method
The nonconforming virtual element method for plate bending problems
Virtual Elements for Linear Elasticity Problems
Divergence free virtual elements for the stokes problem on polygonal meshes
Error Estimate of Fourth-Order Compact Scheme for Linear Schrödinger Equations
A $C^1$ Virtual Element Method for the Cahn--Hilliard Equation with Polygonal Meshes
Nonconforming Finite Element Methods for the Equations of Linear Elasticity
Simple nonconforming quadrilateral Stokes element
Finite difference discretization of the cubic Schrödinger equation
An exact solution for a derivative nonlinear Schrödinger equation
A Space-Time Finite Element Method for the Nonlinear Schrödinger Equation: The Continuous Galerkin Method
A space-time finite element method for the nonlinear Schrödinger equation: the discontinuous Galerkin method
Soliton solutions to the gauged nonlinear Schrödinger equation on the plane
Stability analysis for the virtual element method
The fully nonconforming virtual element method for biharmonic problems
Virtual Elements for the Navier--Stokes Problem on Polygonal Meshes
Conforming and nonconforming virtual element methods for elliptic problems
BASIC PRINCIPLES OF VIRTUAL ELEMENT METHODS
Symplectic Euler Method for Nonlinear High Order Schrödinger Equation with a Trapped Term
Convergence Analysis on Stochastic Collocation Methods for the Linear Schrodinger Equation with Random Inputs
The Divergence-Free Nonconforming Virtual Element for the Stokes Problem
Novel Multi-symplectic Integrators for Nonlinear Fourth-order Schrödinger Equation with Trapped Term
A Stream Virtual Element Formulation of the Stokes Problem on Polygonal Meshes
Dynamics of Rotating Bose--Einstein Condensates and its Efficient and Accurate Numerical Computation

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