The hp- and h-versions of the discontinuous and local discontinuous Galerkin methods for one-dimensional singularly perturbed models

Applied Numerical Mathematics ◽

10.1016/j.apnum.2011.08.001 ◽

2011 ◽

Vol 61 (12) ◽

pp. 1223-1236 ◽

Author(s):

Kassem Mustapha

Keyword(s):

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Singularly Perturbed ◽

Galerkin Methods ◽

One Dimensional ◽

Local Discontinuous Galerkin ◽

Local Discontinuous Galerkin Methods

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Local discontinuous Galerkin methods for moment models in device simulations: formulation and one dimensional results

Electrical Performance of Electronic Packaging IWCE-04 ◽

10.1109/iwce.2004.1407380 ◽

2004 ◽

Author(s):

Yunxian Liu ◽

Chi-Wang Shu

Keyword(s):

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Galerkin Methods ◽

One Dimensional ◽

Local Discontinuous Galerkin ◽

Local Discontinuous Galerkin Methods ◽

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Superconvergence of local discontinuous Galerkin methods for one-dimensional convection–diffusion equations

Computers & Structures ◽

10.1016/j.compstruc.2008.11.012 ◽

2009 ◽

Vol 87 (11-12) ◽

pp. 630-641 ◽

Author(s):

Yingda Cheng ◽

Chi-Wang Shu

Keyword(s):

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Diffusion Equations ◽

Galerkin Methods ◽

One Dimensional ◽

Convection Diffusion ◽

Local Discontinuous Galerkin ◽

Local Discontinuous Galerkin Methods

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Superconvergence of Local Discontinuous Galerkin methods for one-dimensional linear parabolic equations

Mathematics of Computation ◽

10.1090/mcom/2975 ◽

2015 ◽

Vol 85 (297) ◽

pp. 63-84 ◽

Author(s):

Waixiang Cao ◽

Zhimin Zhang

Keyword(s):

Discontinuous Galerkin ◽

Parabolic Equations ◽

Discontinuous Galerkin Methods ◽

Galerkin Methods ◽

One Dimensional ◽

Local Discontinuous Galerkin ◽

Local Discontinuous Galerkin Methods ◽

Linear Parabolic Equations

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Local Discontinuous Galerkin Methods for Moment Models in Device Simulations: Formulation and One Dimensional Results

Journal of Computational Electronics ◽

10.1007/s10825-004-7058-5 ◽

2004 ◽

Vol 3 (3-4) ◽

pp. 263-267 ◽

Author(s):

Yunxian Liu ◽

Chi-Wang Shu

Keyword(s):

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Galerkin Methods ◽

One Dimensional ◽

Local Discontinuous Galerkin ◽

Local Discontinuous Galerkin Methods ◽

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Local Discontinuous Galerkin Methods for One-Dimensional Second Order Fully Nonlinear Elliptic and Parabolic Equations

Journal of Scientific Computing ◽

10.1007/s10915-013-9763-3 ◽

2013 ◽

Vol 59 (1) ◽

pp. 129-157 ◽

Author(s):

Xiaobing Feng ◽

Thomas Lewis

Keyword(s):

Discontinuous Galerkin ◽

Parabolic Equations ◽

Discontinuous Galerkin Methods ◽

Galerkin Methods ◽

Fully Nonlinear ◽

One Dimensional ◽

Local Discontinuous Galerkin ◽

Nonlinear Elliptic ◽

Local Discontinuous Galerkin Methods ◽

Elliptic And Parabolic Equations

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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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Implicit–Explicit Local Discontinuous Galerkin Methods with Generalized Alternating Numerical Fluxes for Convection–Diffusion Problems

Journal of Scientific Computing ◽

10.1007/s10915-019-01072-4 ◽

2019 ◽

Vol 81 (3) ◽

pp. 2080-2114 ◽

Author(s):

Haijin Wang ◽

Qiang Zhang ◽

Chi-Wang Shu

Keyword(s):

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Galerkin Methods ◽

Convection Diffusion ◽

Local Discontinuous Galerkin ◽

Local Discontinuous Galerkin Methods ◽

Numerical Fluxes ◽

Diffusion Problems

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