Energy conserving local discontinuous Galerkin methods for the nonlinear Schrödinger equation with wave operator

DOI10.1007/s10915-014-9977-zzbMath1334.65154OpenAlexW1987077205MaRDI QIDQ898499

N. E. Zubov

Publication date: 9 December 2015

Published in: Journal of Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10915-014-9977-z

zbMATH Keywords

numerical exampleenergy conservationsemidiscretizationoptimal error estimatesCrank-Nicolson method in timelocal discontinuous Galerkin method in spaceSchrödinger equation with wave operator

Mathematics Subject Classification ID

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) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20)

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Cites Work

• Energy conserving local discontinuous Galerkin methods for wave propagation problems
• Discrete-time orthogonal spline collocation methods for the nonlinear Schrödinger equation with wave operator
• A high-order accurate discontinuous finite element method for the numerical solution of the compressible Navier-Stokes equations
• Analysis of some new conservative schemes for nonlinear Schrödinger equation with wave operator
• A Fourier spectral-discontinuous Galerkin method for time-dependent 3-D Schrödinger-Poisson equations with discontinuous potentials
• Comparisons between sine-Gordon and perturbed nonlinear Schrödinger equations for modeling light bullets beyond critical collapse
• TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws. III: One-dimensional systems
• On the nonrelativistic limits of the Klein-Gordon and Dirac equations
• The Runge-Kutta discontinuous Galerkin method for conservation laws. I: Multidimensional systems
• A conservative numerical scheme for a class of nonlinear Schrödinger equation with wave operator.
• Nonrelativistic limit in the energy space for nonlinear Klein-Gordon equations
• Local discontinuous Galerkin methods for nonlinear Schrödinger equations
• Numerical simulation of nonlinear Schrödinger systems: A new conservative scheme
• Modeling light bullets with the two-dimensional sine-Gordon equation
• A compact finite difference scheme for the nonlinear Schrödinger equation with wave operator
• A generalized discontinuous Galerkin (GDG) method for Schrödinger equations with nonsmooth solutions
• Optimal Error Estimates of the Semidiscrete Local Discontinuous Galerkin Methods for High Order Wave Equations
• Uniform Error Estimates of Finite Difference Methods for the Nonlinear Schrödinger Equation with Wave Operator
• Analysis of a Local Discontinuous Galerkin Method for Linear Time-Dependent Fourth-Order Problems
• Nonrelativistic approximation of nonlinear Klein-Gordon equations in two space dimensions
• The Runge-Kutta Local Projection Discontinuous Galerkin Finite Element Method for Conservation Laws. IV: The Multidimensional Case
• TVB Runge-Kutta Local Projection Discontinuous Galerkin Finite Element Method for Conservation Laws II: General Framework
• The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems
• Geometric numerical integration illustrated by the Störmer–Verlet method
• Local Discontinuous Galerkin Methods for the Degasperis-Procesi Equation
• A singular perturbation problem for an envelope equation in plasma physics
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