Reconstructed Discontinuous Galerkin Methods Based on First-Order Hyperbolic System for Advection-Diffusion Equations

23rd AIAA Computational Fluid Dynamics Conference ◽

10.2514/6.2017-3445 ◽

2017 ◽

Cited By ~ 2

Author(s):

Jialin Lou ◽

Lingquan Li ◽

Xiaodong Liu ◽

Hong Luo ◽

Hiroaki Nishikawa

Keyword(s):

Discontinuous Galerkin ◽

Hyperbolic System ◽

Discontinuous Galerkin Methods ◽

Diffusion Equations ◽

Galerkin Methods ◽

First Order ◽

Advection Diffusion

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Reconstructed discontinuous Galerkin methods for linear advection–diffusion equations based on first-order hyperbolic system

Journal of Computational Physics ◽

10.1016/j.jcp.2018.04.058 ◽

2018 ◽

Vol 369 ◽

pp. 103-124 ◽

Cited By ~ 11

Author(s):

Jialin Lou ◽

Lingquan Li ◽

Hong Luo ◽

Hiroaki Nishikawa

Keyword(s):

Discontinuous Galerkin ◽

Hyperbolic System ◽

Discontinuous Galerkin Methods ◽

Diffusion Equations ◽

Galerkin Methods ◽

First Order ◽

Advection Diffusion

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First-Order Hyperbolic System Based Reconstructed Discontinuous Galerkin Methods for Nonlinear Diffusion Equations on Unstructured Grids

2018 AIAA Aerospace Sciences Meeting ◽

10.2514/6.2018-2094 ◽

2018 ◽

Cited By ~ 4

Author(s):

Jialin Lou ◽

Lingquan Li ◽

Hong Luo ◽

Hiroaki Nishikawa

Keyword(s):

Discontinuous Galerkin ◽

Hyperbolic System ◽

Nonlinear Diffusion ◽

Discontinuous Galerkin Methods ◽

Unstructured Grids ◽

Diffusion Equations ◽

Galerkin Methods ◽

Nonlinear Diffusion Equations ◽

First Order

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A Family of Characteristic Discontinuous Galerkin Methods for Transient Advection-Diffusion Equations and Their Optimal-Order L^2 Error Estimates

Communications in Computational Physics ◽

10.4208/cicp.2009.v6.p203 ◽

2009 ◽

pp. 203-230 ◽

Cited By ~ 8

Author(s):

Kaixin Wang ◽

Hong Wang ◽

Mohamed Al-Lawatia ◽

Hongxing Rui

Keyword(s):

Error Estimates ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Diffusion Equations ◽

Optimal Order ◽

Galerkin Methods ◽

Advection Diffusion

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Reconstructed Discontinuous Galerkin Methods for Diffusion Using a First-Order Hyperbolic System Formulation

55th AIAA Aerospace Sciences Meeting ◽

10.2514/6.2017-0310 ◽

2017 ◽

Author(s):

Jialin Lou ◽

Xiaodong Liu ◽

Hong Luo ◽

Hiroaki Nishikawa

Keyword(s):

Discontinuous Galerkin ◽

Hyperbolic System ◽

Discontinuous Galerkin Methods ◽

Galerkin Methods ◽

First Order

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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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Stability analysis and error estimates of local discontinuous Galerkin methods for convection–diffusion equations on overlapping meshes

BIT Numerical Mathematics ◽

10.1007/s10543-019-00757-4 ◽

2019 ◽

Vol 59 (4) ◽

pp. 853-876 ◽

Cited By ~ 1

Author(s):

Jie Du ◽

Yang Yang ◽

Eric Chung

Keyword(s):

Stability Analysis ◽

Error Estimates ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Diffusion Equations ◽

Galerkin Methods ◽

Convection Diffusion ◽

Local Discontinuous Galerkin ◽

Local Discontinuous Galerkin Methods

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Discontinuous Galerkin Methods for Advection-Diffusion-Reaction Problems on Anisotropically Refined Meshes

SIAM Journal on Scientific Computing ◽

10.1137/060672352 ◽

2008 ◽

Vol 30 (1) ◽

pp. 246-271 ◽

Cited By ~ 39

Author(s):

Emmanuil H. Georgoulis ◽

Edward Hall ◽

Paul Houston

Keyword(s):

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Diffusion Reaction ◽

Galerkin Methods ◽

Advection Diffusion ◽

Refined Meshes

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Spacetime discontinuous Galerkin methods for convection-diffusion equations

Bulletin of the Brazilian Mathematical Society New Series ◽

10.1007/s00574-016-0169-3 ◽

2016 ◽

Vol 47 (2) ◽

pp. 561-573 ◽

Cited By ~ 2

Author(s):

Sandra May

Keyword(s):

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Diffusion Equations ◽

Galerkin Methods ◽

Convection Diffusion

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Adaptive discontinuous Galerkin methods for state constrained optimal control problems governed by convection diffusion equations

Computational Optimization and Applications ◽

10.1007/s10589-014-9691-7 ◽

2014 ◽

Vol 62 (1) ◽

pp. 291-321 ◽

Cited By ~ 4

Author(s):

Hamdullah Yücel ◽

Peter Benner

Keyword(s):

Optimal Control ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Optimal Control Problems ◽

Diffusion Equations ◽

Control Problems ◽

Galerkin Methods ◽

Constrained Optimal Control ◽

Convection Diffusion

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Local Discontinuous Galerkin methods for fractional diffusion equations

ESAIM Mathematical Modelling and Numerical Analysis ◽

10.1051/m2an/2013091 ◽

2013 ◽

Vol 47 (6) ◽

pp. 1845-1864 ◽

Cited By ~ 97

Author(s):

W.H. Deng ◽

J.S. Hesthaven

Keyword(s):

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Fractional Diffusion ◽

Diffusion Equations ◽

Galerkin Methods ◽

Fractional Diffusion Equations ◽

Local Discontinuous Galerkin ◽

Local Discontinuous Galerkin Methods

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