High-Order Local Discontinuous Galerkin Algorithm with Time Second-Order Schemes for the Two-Dimensional Nonlinear Fractional Diffusion Equation

Min Zhang; Yang Liu; Hong Li

doi:10.1007/s42967-019-00058-1

High-Order Local Discontinuous Galerkin Algorithm with Time Second-Order Schemes for the Two-Dimensional Nonlinear Fractional Diffusion Equation

Communications on Applied Mathematics and Computation ◽

10.1007/s42967-019-00058-1 ◽

2020 ◽

Vol 2 (4) ◽

pp. 613-640 ◽

Cited By ~ 1

Author(s):

Min Zhang ◽

Yang Liu ◽

Hong Li

Keyword(s):

Diffusion Equation ◽

Discontinuous Galerkin ◽

Fractional Diffusion ◽

Second Order ◽

High Order ◽

Fractional Diffusion Equation ◽

Two Dimensional ◽

Local Discontinuous Galerkin

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A second-order accurate numerical method for the two-dimensional fractional diffusion equation

Journal of Computational Physics ◽

10.1016/j.jcp.2006.05.030 ◽

2007 ◽

Vol 220 (2) ◽

pp. 813-823 ◽

Cited By ~ 214

Author(s):

Charles Tadjeran ◽

Mark M. Meerschaert

Keyword(s):

Diffusion Equation ◽

Numerical Method ◽

Fractional Diffusion ◽

Second Order ◽

Fractional Diffusion Equation ◽

Two Dimensional

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Central local discontinuous Galerkin method for the space fractional diffusion equation

Computers & Mathematics with Applications ◽

10.1016/j.camwa.2019.02.002 ◽

2019 ◽

Vol 78 (5) ◽

pp. 1274-1287 ◽

Cited By ~ 2

Author(s):

Jing Sun ◽

Daxin Nie ◽

Weihua Deng

Keyword(s):

Diffusion Equation ◽

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Local Discontinuous Galerkin Method ◽

Fractional Diffusion ◽

Fractional Diffusion Equation ◽

Local Discontinuous Galerkin ◽

Space Fractional Diffusion Equation

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Local discontinuous Galerkin method for the fractional diffusion equation with integral fractional Laplacian

Computers & Mathematics with Applications ◽

10.1016/j.camwa.2021.11.007 ◽

2021 ◽

Vol 104 ◽

pp. 44-49

Author(s):

Daxin Nie ◽

Weihua Deng

Keyword(s):

Diffusion Equation ◽

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Fractional Laplacian ◽

Local Discontinuous Galerkin Method ◽

Fractional Diffusion ◽

Fractional Diffusion Equation ◽

Local Discontinuous Galerkin

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Compact high-order implicit iterative scheme for the two-dimensional time-fractional diffusion equation

10.1063/5.0075743 ◽

2021 ◽

Author(s):

Muhammad Asim Khan ◽

Norhashidah Hj. Mohd Ali ◽

Nur Nadiah Abd Hamid

Keyword(s):

Diffusion Equation ◽

Iterative Scheme ◽

Fractional Diffusion ◽

High Order ◽

Fractional Diffusion Equation ◽

Two Dimensional ◽

Time Fractional Diffusion Equation ◽

Implicit Iterative Scheme

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Space-dependent source determination in a time-fractional diffusion equation using a local discontinuous Galerkin method

BIT Numerical Mathematics ◽

10.1007/s10543-017-0648-y ◽

2017 ◽

Vol 57 (3) ◽

pp. 685-707 ◽

Cited By ~ 8

Author(s):

S. Yeganeh ◽

R. Mokhtari ◽

J. S. Hesthaven

Keyword(s):

Diffusion Equation ◽

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Local Discontinuous Galerkin Method ◽

Fractional Diffusion ◽

Fractional Diffusion Equation ◽

Local Discontinuous Galerkin ◽

Source Determination ◽

Time Fractional Diffusion Equation

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A local discontinuous Galerkin method for time-fractional diffusion equation with discontinuous coefficient

Applied Numerical Mathematics ◽

10.1016/j.apnum.2019.11.003 ◽

2020 ◽

Vol 151 ◽

pp. 367-379 ◽

Cited By ~ 5

Author(s):

Chaobao Huang ◽

Na An ◽

Xijun Yu

Keyword(s):

Diffusion Equation ◽

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Local Discontinuous Galerkin Method ◽

Fractional Diffusion ◽

Fractional Diffusion Equation ◽

Discontinuous Coefficient ◽

Local Discontinuous Galerkin ◽

Time Fractional Diffusion Equation

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Local discontinuous Galerkin methods for the time tempered fractional diffusion equation

Applied Mathematics and Computation ◽

10.1016/j.amc.2019.124725 ◽

2020 ◽

Vol 365 ◽

pp. 124725

Author(s):

Xiaorui Sun ◽

Can Li ◽

Fengqun Zhao

Keyword(s):

Diffusion Equation ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Fractional Diffusion ◽

Fractional Diffusion Equation ◽

Galerkin Methods ◽

Local Discontinuous Galerkin ◽

Local Discontinuous Galerkin Methods

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High-Order Accurate Runge-Kutta (Local) Discontinuous Galerkin Methods for One- and Two-Dimensional Fractional Diffusion Equations

Numerical Mathematics Theory Methods and Applications ◽

10.4208/nmtma.2012.m1107 ◽

2012 ◽

Vol 5 (3) ◽

pp. 333-358 ◽

Cited By ~ 30

Author(s):

Xia Ji and Huazhong Tang

Keyword(s):

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Fractional Diffusion ◽

High Order ◽

Diffusion Equations ◽

Galerkin Methods ◽

Two Dimensional ◽

Fractional Diffusion Equations ◽

Local Discontinuous Galerkin ◽

Local Discontinuous Galerkin Methods

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Stability and convergence of a local discontinuous Galerkin method for the fractional diffusion equation with distributed order

Journal of Applied Mathematics and Computing ◽

10.1007/s12190-018-1182-z ◽

2018 ◽

Vol 59 (1-2) ◽

pp. 323-341 ◽

Cited By ~ 1

Author(s):

Leilei Wei ◽

Lijie Liu ◽

Huixia Sun

Keyword(s):

Diffusion Equation ◽

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Local Discontinuous Galerkin Method ◽

Fractional Diffusion ◽

Fractional Diffusion Equation ◽

Stability And Convergence ◽

Local Discontinuous Galerkin ◽

Distributed Order

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Convergence analysis of high-order compact alternating direction implicit schemes for the two-dimensional time fractional diffusion equation

Numerical Algorithms ◽

10.1007/s11075-012-9589-3 ◽

2012 ◽

Vol 62 (3) ◽

pp. 383-409 ◽

Cited By ~ 54

Author(s):

Mingrong Cui

Keyword(s):

Diffusion Equation ◽

Convergence Analysis ◽

Fractional Diffusion ◽

High Order ◽

Fractional Diffusion Equation ◽

Two Dimensional ◽

Alternating Direction Implicit ◽

Implicit Schemes ◽

Alternating Direction ◽

Time Fractional Diffusion Equation

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