An ultraweak-local discontinuous Galerkin method for PDEs with high order spatial derivatives

Qi Tao; Yan Xu; Chi-Wang Shu

doi:10.1090/mcom/3562

An ultraweak-local discontinuous Galerkin method for PDEs with high order spatial derivatives

Mathematics of Computation ◽

10.1090/mcom/3562 ◽

2020 ◽

Vol 89 (326) ◽

pp. 2753-2783 ◽

Cited By ~ 2

Author(s):

Qi Tao ◽

Yan Xu ◽

Chi-Wang Shu

Keyword(s):

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Local Discontinuous Galerkin Method ◽

High Order ◽

Local Discontinuous Galerkin ◽

Spatial Derivatives

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Positivity preserving high-order local discontinuous Galerkin method for parabolic equations with blow-up solutions

Journal of Computational Physics ◽

10.1016/j.jcp.2015.02.041 ◽

2015 ◽

Vol 289 ◽

pp. 181-195 ◽

Cited By ~ 17

Author(s):

Li Guo ◽

Yang Yang

Keyword(s):

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Parabolic Equations ◽

Blow Up ◽

Local Discontinuous Galerkin Method ◽

High Order ◽

Positivity Preserving ◽

Local Discontinuous Galerkin

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A High Order Adaptive Time-Stepping Strategy and Local Discontinuous Galerkin Method for the Modified Phase Field Crystal Equation

Communications in Computational Physics ◽

10.4208/cicp.oa-2017-0074 ◽

2018 ◽

Vol 24 (1) ◽

Cited By ~ 3

Author(s):

Ruihan Guo ◽

Yan Xu

Keyword(s):

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Phase Field ◽

Local Discontinuous Galerkin Method ◽

High Order ◽

Time Stepping ◽

Local Discontinuous Galerkin ◽

Adaptive Time ◽

Adaptive Time Stepping

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High‐order local discontinuous Galerkin method for a fractal mobile/immobile transport equation with the Caputo–Fabrizio fractional derivative

Numerical Methods for Partial Differential Equations ◽

10.1002/num.22366 ◽

2019 ◽

Vol 35 (4) ◽

pp. 1588-1612 ◽

Cited By ~ 1

Author(s):

Min Zhang ◽

Yang Liu ◽

Hong Li

Keyword(s):

Fractional Derivative ◽

Galerkin Method ◽

Transport Equation ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Local Discontinuous Galerkin Method ◽

High Order ◽

Local Discontinuous Galerkin

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High-order local discontinuous Galerkin method for simulating wormhole propagation

Journal of Computational and Applied Mathematics ◽

10.1016/j.cam.2018.10.021 ◽

2019 ◽

Vol 350 ◽

pp. 247-261 ◽

Cited By ~ 4

Author(s):

Hui Guo ◽

Lulu Tian ◽

Ziyao Xu ◽

Yang Yang ◽

Ning Qi

Keyword(s):

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Local Discontinuous Galerkin Method ◽

High Order ◽

Local Discontinuous Galerkin

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Local Discontinuous Galerkin Method and High Order Semi-Implicit Scheme for the Phase Field Crystal Equation

SIAM Journal on Scientific Computing ◽

10.1137/15m1038803 ◽

2016 ◽

Vol 38 (1) ◽

pp. A105-A127 ◽

Cited By ~ 16

Author(s):

Ruihan Guo ◽

Yan Xu

Keyword(s):

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Phase Field ◽

Local Discontinuous Galerkin Method ◽

High Order ◽

Implicit Scheme ◽

Local Discontinuous Galerkin ◽

Phase Field Crystal

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High-order local discontinuous Galerkin method combined with WSGD-approximation for a fractional subdiffusion equation

Computers & Mathematics with Applications ◽

10.1016/j.camwa.2016.08.015 ◽

2017 ◽

Vol 73 (6) ◽

pp. 1298-1314 ◽

Cited By ~ 29

Author(s):

Yang Liu ◽

Min Zhang ◽

Hong Li ◽

Jichun Li

Keyword(s):

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Local Discontinuous Galerkin Method ◽

High Order ◽

Local Discontinuous Galerkin ◽

Subdiffusion Equation

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Convergence and Superconvergence of the Local Discontinuous Galerkin Method for Semilinear Second-Order Elliptic Problems on Cartesian Grids

Communications on Applied Mathematics and Computation ◽

10.1007/s42967-021-00123-8 ◽

2021 ◽

Author(s):

Mahboub Baccouch

Keyword(s):

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Elliptic Problems ◽

Local Discontinuous Galerkin Method ◽

Second Order ◽

Cartesian Grids ◽

Local Discontinuous Galerkin ◽

Convergence And Superconvergence ◽

Second Order Elliptic Problems

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Solving a non-linear fractional convection-diffusion equation using local discontinuous Galerkin method

Applied Numerical Mathematics ◽

10.1016/j.apnum.2021.02.003 ◽

2021 ◽

Vol 165 ◽

pp. 22-34

Author(s):

Hamid Safdari ◽

Majid Rajabzadeh ◽

Moein Khalighi

Keyword(s):

Diffusion Equation ◽

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Local Discontinuous Galerkin Method ◽

Convection Diffusion ◽

Convection Diffusion Equation ◽

Local Discontinuous Galerkin ◽

Non Linear

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Local discontinuous Galerkin method for distributed‐order time‐fractional diffusion‐wave equation: Application of Laplace transform

Mathematical Methods in the Applied Sciences ◽

10.1002/mma.7077 ◽

2020 ◽

Author(s):

Hadi Mohammadi‐Firouzjaei ◽

Hojatollah Adibi ◽

Mehdi Dehghan

Keyword(s):

Wave Equation ◽

Laplace Transform ◽

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Local Discontinuous Galerkin Method ◽

Fractional Diffusion ◽

Diffusion Wave ◽

Local Discontinuous Galerkin ◽

Distributed Order

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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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