Superconvergence of Local Discontinuous Galerkin Method for One-Dimensional Linear Schrödinger Equations

Lingling Zhou; Yan Xu; Zhimin Zhang; Waixiang Cao

doi:10.1007/s10915-017-0362-6

Superconvergence of Local Discontinuous Galerkin Method for One-Dimensional Linear Schrödinger Equations

Journal of Scientific Computing ◽

10.1007/s10915-017-0362-6 ◽

2017 ◽

Vol 73 (2-3) ◽

pp. 1290-1315 ◽

Cited By ~ 6

Author(s):

Lingling Zhou ◽

Yan Xu ◽

Zhimin Zhang ◽

Waixiang Cao

Keyword(s):

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Local Discontinuous Galerkin Method ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

One Dimensional ◽

Local Discontinuous Galerkin

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A Local Discontinuous Galerkin Method with Generalized Alternating Fluxes for 2D Nonlinear Schrödinger Equations

Communications on Applied Mathematics and Computation ◽

10.1007/s42967-020-00100-7 ◽

2021 ◽

Author(s):

Hongjuan Zhang ◽

Boying Wu ◽

Xiong Meng

Keyword(s):

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Local Discontinuous Galerkin Method ◽

Nonlinear Schrödinger Equations ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Nonlinear Schrödinger ◽

Local Discontinuous Galerkin ◽

Nonlinear Schrodinger Equations

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Error estimates and post-processing of local discontinuous Galerkin method for Schrödinger equations

Journal of Computational and Applied Mathematics ◽

10.1016/j.cam.2019.01.033 ◽

2019 ◽

Vol 356 ◽

pp. 198-218

Author(s):

Qi Tao ◽

Yinhua Xia

Keyword(s):

Galerkin Method ◽

Error Estimates ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Local Discontinuous Galerkin Method ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Post Processing ◽

Local Discontinuous Galerkin

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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 ◽

Cited By ~ 10

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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On the Convergence of the Local Discontinuous Galerkin Method Applied to a Stationary One Dimensional Fractional Diffusion Problem

Journal of Scientific Computing ◽

10.1007/s10915-020-01335-5 ◽

2020 ◽

Vol 85 (2) ◽

Author(s):

P. Castillo ◽

S. Gómez

Keyword(s):

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Local Discontinuous Galerkin Method ◽

Fractional Diffusion ◽

Diffusion Problem ◽

One Dimensional ◽

Local Discontinuous Galerkin

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Optimal energy-conserving local discontinuous Galerkin method for the one-dimensional sine-Gordon equation

International Journal of Computer Mathematics ◽

10.1080/00207160.2015.1105364 ◽

2015 ◽

Vol 94 (2) ◽

pp. 316-344 ◽

Cited By ~ 7

Author(s):

Mahboub Baccouch

Keyword(s):

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Gordon Equation ◽

Local Discontinuous Galerkin Method ◽

Sine Gordon Equation ◽

One Dimensional ◽

Local Discontinuous Galerkin ◽

Energy Conserving ◽

The One

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Local Analysis of the Local Discontinuous Galerkin Method with Generalized Alternating Numerical Flux for One-Dimensional Singularly Perturbed Problem

Journal of Scientific Computing ◽

10.1007/s10915-017-0378-y ◽

2017 ◽

Vol 72 (2) ◽

pp. 792-819 ◽

Cited By ~ 9

Author(s):

Yao Cheng ◽

Qiang Zhang

Keyword(s):

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Local Discontinuous Galerkin Method ◽

Singularly Perturbed ◽

Singularly Perturbed Problem ◽

Local Analysis ◽

One Dimensional ◽

Numerical Flux ◽

Local Discontinuous Galerkin

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Superconvergence of the Local Discontinuous Galerkin Method for One Dimensional Nonlinear Convection-Diffusion Equations

Journal of Scientific Computing ◽

10.1007/s10915-021-01446-7 ◽

2021 ◽

Vol 87 (1) ◽

Author(s):

Xiaobin Liu ◽

Dazhi Zhang ◽

Xiong Meng ◽

Boying Wu

Keyword(s):

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Local Discontinuous Galerkin Method ◽

Diffusion Equations ◽

Nonlinear Convection ◽

One Dimensional ◽

Convection Diffusion ◽

Local Discontinuous Galerkin

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Superconvergence Analysis of the Ultra-Weak Local Discontinuous Galerkin Method for One Dimensional Linear Fifth Order Equations

Journal of Scientific Computing ◽

10.1007/s10915-021-01579-9 ◽

2021 ◽

Vol 88 (3) ◽

Author(s):

Qi Tao ◽

Waixiang Cao ◽

Zhimin Zhang

Keyword(s):

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Local Discontinuous Galerkin Method ◽

One Dimensional ◽

Local Discontinuous Galerkin ◽

Fifth Order

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Superconvergence of the local discontinuous galerkin method applied to the one-dimensional second-order wave equation

Numerical Methods for Partial Differential Equations ◽

10.1002/num.21840 ◽

2013 ◽

Vol 30 (3) ◽

pp. 862-901 ◽

Cited By ~ 13

Author(s):

Mahboub Baccouch

Keyword(s):

Wave Equation ◽

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Local Discontinuous Galerkin Method ◽

Second Order ◽

One Dimensional ◽

Local Discontinuous Galerkin ◽

Second Order Wave Equation ◽

The One

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Analysis of Sharp Superconvergence of Local Discontinuous Galerkin Method for One-Dimensional Linear Parabolic Equations

Journal of Computational Mathematics ◽

10.4208/jcm.1502-m2014-0001 ◽

2015 ◽

Vol 33 (3) ◽

pp. 323-340 ◽

Cited By ~ 19

Author(s):

Yang Yang and Chi-Wang Shu

Keyword(s):

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Parabolic Equations ◽

Local Discontinuous Galerkin Method ◽

One Dimensional ◽

Local Discontinuous Galerkin ◽

Linear Parabolic Equations

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