Higher order uniformly convergent continuous/discontinuous Galerkin methods for singularly perturbed problems of convection-diffusion type

Applied Numerical Mathematics ◽

10.1016/j.apnum.2013.10.001 ◽

2014 ◽

Vol 76 ◽

pp. 48-59 ◽

Author(s):

Peng Zhu ◽

Shenglan Xie

Keyword(s):

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Higher Order ◽

Singularly Perturbed ◽

Galerkin Methods ◽

Singularly Perturbed Problems ◽

Diffusion Type ◽

Convection Diffusion ◽

Uniformly Convergent

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A uniformly convergent continuous–discontinuous Galerkin method for singularly perturbed problems of convection–diffusion type

Applied Mathematics and Computation ◽

10.1016/j.amc.2010.11.033 ◽

2011 ◽

Vol 217 (9) ◽

pp. 4781-4790 ◽

Author(s):

Peng Zhu ◽

Ziqing Xie ◽

Shuzi Zhou

Keyword(s):

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Singularly Perturbed ◽

Singularly Perturbed Problems ◽

Diffusion Type ◽

Convection Diffusion ◽

Uniformly Convergent

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Higher order uniformly convergent NIPG methods for 1-d singularly perturbed problems of convection–diffusion type

Applied Mathematical Modelling ◽

10.1016/j.apm.2015.02.021 ◽

2015 ◽

Vol 39 (22) ◽

pp. 6806-6816 ◽

Author(s):

Peng Zhu ◽

Yubo Yang ◽

Yunhui Yin

Keyword(s):

Higher Order ◽

Singularly Perturbed ◽

Singularly Perturbed Problems ◽

Diffusion Type ◽

Convection Diffusion ◽

Uniformly Convergent

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Discontinuous Galerkin methods with interior penalties on graded meshes for 2D singularly perturbed convection–diffusion problems

Applied Numerical Mathematics ◽

10.1016/j.apnum.2016.09.004 ◽

2017 ◽

Vol 111 ◽

pp. 36-48 ◽

Author(s):

Yubo Yang ◽

Peng Zhu

Keyword(s):

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Singularly Perturbed ◽

Galerkin Methods ◽

Convection Diffusion ◽

Graded Meshes ◽

Interior Penalties ◽

Diffusion Problems

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Local analysis of discontinuous Galerkin methods applied to singularly perturbed problems

Journal of Numerical Mathematics ◽

10.1515/156939506776382157 ◽

2006 ◽

Vol 14 (1) ◽

Author(s):

J. Guzmán

Keyword(s):

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Singularly Perturbed ◽

Local Analysis ◽

Galerkin Methods ◽

Singularly Perturbed Problems

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Local analysis of discontinuous Galerkin methods applied to singularly perturbed problems

Journal of Numerical Mathematics ◽

10.1163/156939506776382157 ◽

2006 ◽

Vol 14 (1) ◽

pp. 41-56 ◽

Author(s):

J. Guzm´n

Keyword(s):

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Singularly Perturbed ◽

Local Analysis ◽

Galerkin Methods ◽

Singularly Perturbed Problems

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A unified framework for time-dependent singularly perturbed problems with discontinuous Galerkin methods in time

Mathematics of Computation ◽

10.1090/mcom/3326 ◽

2018 ◽

Vol 87 (313) ◽

pp. 2113-2132 ◽

Author(s):

Sebastian Franz ◽

Gunar Matthies

Keyword(s):

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Singularly Perturbed ◽

Time Dependent ◽

Galerkin Methods ◽

Unified Framework ◽

Singularly Perturbed Problems

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Analysis of direct discontinuous Galerkin methods for multi-dimensional convection–diffusion equations

Numerische Mathematik ◽

10.1007/s00211-021-01183-x ◽

2021 ◽

Vol 147 (4) ◽

pp. 839-867

Author(s):

Hailiang Liu

Keyword(s):

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Diffusion Equations ◽

Galerkin Methods ◽

Convection Diffusion

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hp-adaptive discontinuous Galerkin methods for non-stationary convection–diffusion problems

Computers & Mathematics with Applications ◽

10.1016/j.camwa.2019.04.002 ◽

2019 ◽

Vol 78 (9) ◽

pp. 3090-3104 ◽

Author(s):

A. Cangiani ◽

E.H. Georgoulis ◽

S. Giani ◽

S. Metcalfe

Keyword(s):

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Galerkin Methods ◽

Stationary Convection ◽

Convection Diffusion ◽

Diffusion Problems

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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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Superconvergence of Discontinuous Galerkin Methods for Convection-Diffusion Problems

Journal of Scientific Computing ◽

10.1007/s10915-009-9288-y ◽

2009 ◽

Vol 41 (1) ◽

pp. 70-93 ◽

Author(s):

Zuozheng Zhang ◽

Ziqing Xie ◽

Zhimin Zhang

Keyword(s):

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Galerkin Methods ◽

Convection Diffusion ◽

Diffusion Problems

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