A conservative local discontinuous Galerkin method for the solution of nonlinear Schrödinger equation in two dimensions

Science China Mathematics ◽

10.1007/s11425-016-9118-x ◽

2017 ◽

Vol 60 (12) ◽

pp. 2515-2530 ◽

Author(s):

RongPei Zhang ◽

XiJun Yu ◽

MingJun Li ◽

XiangGui Li

Keyword(s):

Schrödinger Equation ◽

Galerkin Method ◽

Discontinuous Galerkin ◽

Nonlinear Schrödinger Equation ◽

Discontinuous Galerkin Method ◽

Schrodinger Equation ◽

Local Discontinuous Galerkin Method ◽

Nonlinear Schrodinger Equation ◽

Two Dimensions ◽

Local Discontinuous Galerkin

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Mean-square convergence of a symplectic local discontinuous Galerkin method applied to stochastic linear Schrödinger equation

IMA Journal of Numerical Analysis ◽

10.1093/imanum/drw023 ◽

2016 ◽

pp. drw023

Author(s):

Chuchu Chen ◽

Jialin Hong ◽

Lihai Ji

Keyword(s):

Schrödinger Equation ◽

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Schrodinger Equation ◽

Local Discontinuous Galerkin Method ◽

Mean Square ◽

Local Discontinuous Galerkin ◽

Mean Square Convergence

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Optimal error estimate of conservative local discontinuous Galerkin method for nonlinear Schrödinger equation

Applied Numerical Mathematics ◽

10.1016/j.apnum.2018.01.004 ◽

2018 ◽

Vol 127 ◽

pp. 164-178 ◽

Author(s):

Jialin Hong ◽

Lihai Ji ◽

Zhihui Liu

Keyword(s):

Error Estimate ◽

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Schrodinger Equation ◽

Local Discontinuous Galerkin Method ◽

Nonlinear Schrodinger Equation ◽

Optimal Error Estimate ◽

Optimal Error ◽

Local Discontinuous Galerkin

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The WKB Local Discontinuous Galerkin Method for the Simulation of Schrödinger Equation in a Resonant Tunneling Diode

Journal of Scientific Computing ◽

10.1007/s10915-008-9237-1 ◽

2008 ◽

Vol 40 (1-3) ◽

pp. 360-374 ◽

Author(s):

Wei Wang ◽

Chi-Wang Shu

Keyword(s):

Schrödinger Equation ◽

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Resonant Tunneling ◽

Schrodinger Equation ◽

Local Discontinuous Galerkin Method ◽

Resonant Tunneling Diode ◽

Local Discontinuous Galerkin ◽

Tunneling Diode

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Analysis of an implicit fully discrete local discontinuous Galerkin method for the time-fractional Schrödinger equation

Finite Elements in Analysis and Design ◽

10.1016/j.finel.2012.03.008 ◽

2012 ◽

Vol 59 ◽

pp. 28-34 ◽

Author(s):

Leilei Wei ◽

Yinnian He ◽

Xindong Zhang ◽

Shaoli Wang

Keyword(s):

Schrödinger Equation ◽

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Schrodinger Equation ◽

Local Discontinuous Galerkin Method ◽

Fractional Schrödinger Equation ◽

Fully Discrete ◽

Local Discontinuous Galerkin ◽

Fractional Schrodinger Equation

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Conservative local discontinuous Galerkin methods for the cubic-quintic nonlinear Schrödinger equation

Optik ◽

10.1016/j.ijleo.2020.165821 ◽

2021 ◽

Vol 226 ◽

pp. 165821

Author(s):

He Yang

Keyword(s):

Schrödinger Equation ◽

Discontinuous Galerkin ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Discontinuous Galerkin Methods ◽

Nonlinear Schrodinger Equation ◽

Galerkin Methods ◽

Local Discontinuous Galerkin ◽

Local Discontinuous Galerkin Methods ◽

Quintic Nonlinear Schrödinger Equation

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A space-time finite element method for the nonlinear Schrödinger equation: the discontinuous Galerkin method

Mathematics of Computation ◽

10.1090/s0025-5718-98-00946-6 ◽

1998 ◽

Vol 67 (222) ◽

pp. 479-500 ◽

Author(s):

Ohannes Karakashian ◽

Charalambos Makridakis

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Schrödinger Equation ◽

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

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Convergence and Superconvergence of the Local Discontinuous Galerkin Method for Semilinear Second-Order Elliptic Problems on Cartesian Grids

Communications on Applied Mathematics and Computation ◽

10.1007/s42967-021-00123-8 ◽

2021 ◽

Author(s):

Mahboub Baccouch

Keyword(s):

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Elliptic Problems ◽

Local Discontinuous Galerkin Method ◽

Second Order ◽

Cartesian Grids ◽

Local Discontinuous Galerkin ◽

Convergence And Superconvergence ◽

Second Order Elliptic Problems

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Solving a non-linear fractional convection-diffusion equation using local discontinuous Galerkin method

Applied Numerical Mathematics ◽

10.1016/j.apnum.2021.02.003 ◽

2021 ◽

Vol 165 ◽

pp. 22-34

Author(s):

Hamid Safdari ◽

Majid Rajabzadeh ◽

Moein Khalighi

Keyword(s):

Diffusion Equation ◽

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Local Discontinuous Galerkin Method ◽

Convection Diffusion ◽

Convection Diffusion Equation ◽

Local Discontinuous Galerkin ◽

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Local discontinuous Galerkin method for distributed‐order time‐fractional diffusion‐wave equation: Application of Laplace transform

Mathematical Methods in the Applied Sciences ◽

10.1002/mma.7077 ◽

2020 ◽

Author(s):

Hadi Mohammadi‐Firouzjaei ◽

Hojatollah Adibi ◽

Mehdi Dehghan

Keyword(s):

Wave Equation ◽

Laplace Transform ◽

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Local Discontinuous Galerkin Method ◽

Fractional Diffusion ◽

Diffusion Wave ◽

Local Discontinuous Galerkin ◽

Distributed Order

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A fully discrete local discontinuous Galerkin method for one-dimensional time-fractional Fisher's equation

International Journal of Computer Mathematics ◽

10.1080/00207160.2013.866233 ◽

2014 ◽

Vol 91 (9) ◽

pp. 2021-2038 ◽

Author(s):

Xindong Zhang ◽

Yinnian He ◽

Leilei Wei ◽

Bo Tang ◽

Shaoli Wang

Keyword(s):

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Local Discontinuous Galerkin Method ◽

One Dimensional ◽

Fisher’S Equation ◽

Fully Discrete ◽

Local Discontinuous Galerkin ◽

Fisher's Equation

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