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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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 ◽

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 of the semi-discrete local discontinuous Galerkin method for nonlinear convection–diffusion and KdV equations

Computer Methods in Applied Mechanics and Engineering ◽

10.1016/j.cma.2006.10.043 ◽

2007 ◽

Vol 196 (37-40) ◽

pp. 3805-3822 ◽

Author(s):

Yan Xu ◽

Chi-Wang Shu

Keyword(s):

Galerkin Method ◽

Error Estimates ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Local Discontinuous Galerkin Method ◽

Nonlinear Convection ◽

Convection Diffusion ◽

Local Discontinuous Galerkin ◽

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Optimal error estimates of the local discontinuous Galerkin method for nonlinear second‐order elliptic problems on Cartesian grids

Numerical Methods for Partial Differential Equations ◽

10.1002/num.22538 ◽

2020 ◽

Vol 37 (1) ◽

pp. 505-532

Author(s):

Mahboub Baccouch

Keyword(s):

Galerkin Method ◽

Error Estimates ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Local Discontinuous Galerkin Method ◽

Optimal Error Estimates ◽

Cartesian Grids ◽

Optimal Error ◽

Local Discontinuous Galerkin ◽

Second Order Elliptic Problems

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Optimal Error Estimates of the Local Discontinuous Galerkin Method for Surface Diffusion of Graphs on Cartesian Meshes

Journal of Scientific Computing ◽

10.1007/s10915-011-9492-4 ◽

2011 ◽

Vol 51 (1) ◽

pp. 1-27 ◽

Author(s):

Liangyue Ji ◽

Yan Xu

Keyword(s):

Galerkin Method ◽

Surface Diffusion ◽

Error Estimates ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Local Discontinuous Galerkin Method ◽

Optimal Error Estimates ◽

Optimal Error ◽

Local Discontinuous Galerkin ◽

Cartesian Meshes

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Two Efficient and Reliable a posteriori Error Estimates for the Local Discontinuous Galerkin Method Applied to Linear Elliptic Problems on Cartesian Grids

Journal of Scientific Computing ◽

10.1007/s10915-021-01497-w ◽

2021 ◽

Vol 87 (3) ◽

Author(s):

Mahboub Baccouch

Keyword(s):

Galerkin Method ◽

Error Estimates ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

A Posteriori Error Estimates ◽

Posteriori Error ◽

Local Discontinuous Galerkin Method ◽

A Posteriori ◽

A Posteriori Error ◽

Local Discontinuous Galerkin

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Optimal a priori error estimates for the $hp$-version of the local discontinuous Galerkin method for convection--diffusion problems

Mathematics of Computation ◽

10.1090/s0025-5718-01-01317-5 ◽

2001 ◽

Vol 71 (238) ◽

pp. 455-479 ◽

Author(s):

Paul Castillo ◽

Bernardo Cockburn ◽

Dominik Schötzau ◽

Christoph Schwab

Keyword(s):

Galerkin Method ◽

Error Estimates ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

A Priori ◽

Local Discontinuous Galerkin Method ◽

Convection Diffusion ◽

Local Discontinuous Galerkin ◽

Priori Error Estimates ◽

Diffusion Problems

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Asymptotically Exact Posteriori Error Estimates for the Local Discontinuous Galerkin Method Applied to Nonlinear Convection–Diffusion Problems

Journal of Scientific Computing ◽

10.1007/s10915-018-0687-9 ◽

2018 ◽

Vol 76 (3) ◽

pp. 1868-1904 ◽

Author(s):

Mahboub Baccouch

Keyword(s):

Galerkin Method ◽

Error Estimates ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Posteriori Error ◽

Local Discontinuous Galerkin Method ◽

Nonlinear Convection ◽

Convection Diffusion ◽

Local Discontinuous Galerkin ◽

Diffusion Problems

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A priori error estimates for interior penalty versions of the local discontinuous Galerkin method applied to transport equations

Numerical Methods for Partial Differential Equations ◽

10.1002/num.1026 ◽

2001 ◽

Vol 17 (6) ◽

pp. 545-564 ◽

Author(s):

Clint Dawson ◽

Jennifer Proft

Keyword(s):

Galerkin Method ◽

Error Estimates ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

A Priori ◽

Local Discontinuous Galerkin Method ◽

A Priori Error Estimates ◽

Interior Penalty ◽

Local Discontinuous Galerkin ◽

Priori Error Estimates

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Local and pointwise error estimates of the local discontinuous Galerkin method applied to the Stokes problem

Mathematics of Computation ◽

10.1090/s0025-5718-08-02067-x ◽

2008 ◽

Vol 77 (263) ◽

pp. 1293-1322 ◽

Author(s):

J. Guzmán

Keyword(s):

Galerkin Method ◽

Error Estimates ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Stokes Problem ◽

Local Discontinuous Galerkin Method ◽

Local Discontinuous Galerkin ◽

Pointwise Error ◽

Pointwise Error Estimates

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