Energy Conserving Local Discontinuous Galerkin Methods for the Nonlinear Schrödinger Equation with Wave Operator

Journal of Scientific Computing ◽

10.1007/s10915-014-9977-z ◽

2014 ◽

Vol 65 (2) ◽

pp. 622-647 ◽

Author(s):

Li Guo ◽

Yan Xu

Keyword(s):

Schrödinger Equation ◽

Discontinuous Galerkin ◽

Wave Operator ◽

Schrodinger Equation ◽

Discontinuous Galerkin Methods ◽

Nonlinear Schrodinger Equation ◽

Galerkin Methods ◽

Local Discontinuous Galerkin ◽

Local Discontinuous Galerkin Methods ◽

Energy Conserving

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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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Energy conserving local discontinuous Galerkin methods for the improved Boussinesq equation

Journal of Computational Physics ◽

10.1016/j.jcp.2019.109002 ◽

2020 ◽

Vol 401 ◽

pp. 109002 ◽

Author(s):

Xiaole Li ◽

Weizhou Sun ◽

Yulong Xing ◽

Ching-Shan Chou

Keyword(s):

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Boussinesq Equation ◽

Galerkin Methods ◽

Local Discontinuous Galerkin ◽

Local Discontinuous Galerkin Methods ◽

Energy Conserving

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Optimal Energy Conserving and Energy Dissipative Local Discontinuous Galerkin Methods for the Benjamin–Bona–Mahony Equation

Journal of Scientific Computing ◽

10.1007/s10915-020-01172-6 ◽

2020 ◽

Vol 83 (1) ◽

Author(s):

Xiaole Li ◽

Yulong Xing ◽

Ching-Shan Chou

Keyword(s):

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Galerkin Methods ◽

Local Discontinuous Galerkin ◽

Optimal Energy ◽

Local Discontinuous Galerkin Methods ◽

Energy Conserving

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Optimal energy conserving local discontinuous Galerkin methods for second-order wave equation in heterogeneous media

Journal of Computational Physics ◽

10.1016/j.jcp.2014.04.009 ◽

2014 ◽

Vol 272 ◽

pp. 88-107 ◽

Author(s):

Ching-Shan Chou ◽

Chi-Wang Shu ◽

Yulong Xing

Keyword(s):

Wave Equation ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Heterogeneous Media ◽

Second Order ◽

Galerkin Methods ◽

Local Discontinuous Galerkin ◽

Local Discontinuous Galerkin Methods ◽

Energy Conserving ◽

Second Order Wave Equation

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Optimal Energy Conserving Local Discontinuous Galerkin Methods for Elastodynamics: Semi and Fully Discrete Error Analysis

Journal of Scientific Computing ◽

10.1007/s10915-021-01418-x ◽

2021 ◽

Vol 87 (1) ◽

Author(s):

Ruchi Guo ◽

Yulong Xing

Keyword(s):

Error Analysis ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Galerkin Methods ◽

Fully Discrete ◽

Local Discontinuous Galerkin ◽

Optimal Energy ◽

Local Discontinuous Galerkin Methods ◽

Energy Conserving

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Energy conserving local discontinuous Galerkin methods for wave propagation problems

Inverse Problems & Imaging ◽

10.3934/ipi.2013.7.967 ◽

2013 ◽

Vol 7 (3) ◽

pp. 967-986 ◽

Author(s):

Yulong Xing ◽

◽

Ching-Shan Chou ◽

Chi-Wang Shu ◽

◽

...

Keyword(s):

Wave Propagation ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Galerkin Methods ◽

Local Discontinuous Galerkin ◽

Local Discontinuous Galerkin Methods ◽

Energy Conserving

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Local Discontinuous Galerkin Methods to a Dispersive System of KdV-Type Equations

Journal of Scientific Computing ◽

10.1007/s10915-020-01370-2 ◽

2021 ◽

Vol 86 (1) ◽

Author(s):

Chao Zhang ◽

Yan Xu ◽

Yinhua Xia

Keyword(s):

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Galerkin Methods ◽

Local Discontinuous Galerkin ◽

Local Discontinuous Galerkin Methods ◽

Dispersive System ◽

Kdv Type Equations

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Local discontinuous Galerkin methods for the Kuramoto–Sivashinsky equations and the Ito-type coupled KdV equations

Computer Methods in Applied Mechanics and Engineering ◽

10.1016/j.cma.2005.06.021 ◽

2006 ◽

Vol 195 (25-28) ◽

pp. 3430-3447 ◽

Author(s):

Yan Xu ◽

Chi-Wang Shu

Keyword(s):

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Galerkin Methods ◽

Local Discontinuous Galerkin ◽

Kdv Equations ◽

Local Discontinuous Galerkin Methods ◽

Coupled Kdv Equations

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Local discontinuous Galerkin methods with implicit-explicit time-marching for multi-dimensional convection-diffusion problems

ESAIM Mathematical Modelling and Numerical Analysis ◽

10.1051/m2an/2015068 ◽

2016 ◽

Vol 50 (4) ◽

pp. 1083-1105 ◽

Author(s):

Haijin Wang ◽

Shiping Wang ◽

Qiang Zhang ◽

Chi-Wang Shu

Keyword(s):

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Galerkin Methods ◽

Convection Diffusion ◽

Local Discontinuous Galerkin ◽

Local Discontinuous Galerkin Methods ◽

Time Marching ◽

Diffusion Problems

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Efficient High Order Semi-implicit Time Discretization and Local Discontinuous Galerkin Methods for Highly Nonlinear PDEs

Journal of Scientific Computing ◽

10.1007/s10915-016-0170-4 ◽

2016 ◽

Vol 68 (3) ◽

pp. 1029-1054 ◽

Author(s):

Ruihan Guo ◽

Francis Filbet ◽

Yan Xu

Keyword(s):

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Time Discretization ◽

Nonlinear Pdes ◽

Implicit Time ◽

Galerkin Methods ◽

Local Discontinuous Galerkin ◽

Local Discontinuous Galerkin Methods ◽

Highly Nonlinear

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