Uniform convergence for a discontinuous Galerkin, time-stepping method applied to a fractional diffusion equation

K. Mustapha; W. McLean

doi:10.1093/imanum/drr027

Uniform convergence for a discontinuous Galerkin, time-stepping method applied to a fractional diffusion equation

IMA Journal of Numerical Analysis ◽

10.1093/imanum/drr027 ◽

2011 ◽

Vol 32 (3) ◽

pp. 906-925 ◽

Cited By ~ 36

Author(s):

K. Mustapha ◽

W. McLean

Keyword(s):

Diffusion Equation ◽

Uniform Convergence ◽

Discontinuous Galerkin ◽

Fractional Diffusion ◽

Fractional Diffusion Equation ◽

Time Stepping

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Time-stepping discontinuous Galerkin approximation of optimal control problem governed by time fractional diffusion equation

Numerical Algorithms ◽

10.1007/s11075-017-0445-3 ◽

2017 ◽

Vol 79 (2) ◽

pp. 437-455 ◽

Cited By ~ 8

Author(s):

Zhaojie Zhou ◽

Chenyang Zhang

Keyword(s):

Optimal Control ◽

Optimal Control Problem ◽

Diffusion Equation ◽

Control Problem ◽

Discontinuous Galerkin ◽

Galerkin Approximation ◽

Fractional Diffusion ◽

Fractional Diffusion Equation ◽

Time Stepping ◽

Time Fractional Diffusion Equation

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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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Piecewise-linear, discontinuous Galerkin method for a fractional diffusion equation

Numerical Algorithms ◽

10.1007/s11075-010-9379-8 ◽

2010 ◽

Vol 56 (2) ◽

pp. 159-184 ◽

Cited By ~ 54

Author(s):

Kassem Mustapha ◽

William McLean

Keyword(s):

Diffusion Equation ◽

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Piecewise Linear ◽

Fractional Diffusion ◽

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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A direct discontinuous Galerkin method for a time-fractional diffusion equation with a Robin boundary condition

Applied Numerical Mathematics ◽

10.1016/j.apnum.2018.08.006 ◽

2019 ◽

Vol 135 ◽

pp. 15-29 ◽

Cited By ~ 7

Author(s):

Chaobao Huang ◽

Martin Stynes

Keyword(s):

Boundary Condition ◽

Diffusion Equation ◽

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Robin Boundary Condition ◽

Fractional Diffusion ◽

Fractional Diffusion Equation ◽

Time Fractional Diffusion Equation ◽

Robin Boundary

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Direct discontinuous Galerkin method for solving nonlinear time fractional diffusion equation with weak singularity solution

Applied Mathematics Letters ◽

10.1016/j.aml.2019.106111 ◽

2020 ◽

Vol 102 ◽

pp. 106111 ◽

Cited By ~ 4

Author(s):

Jincheng Ren ◽

Chaobao Huang ◽

Na An

Keyword(s):

Diffusion Equation ◽

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Fractional Diffusion ◽

Fractional Diffusion Equation ◽

Weak Singularity ◽

Time Fractional Diffusion Equation

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

Complex Variables and Elliptic Equations ◽

10.1080/17476933.2019.1655552 ◽

2019 ◽

Vol 65 (9) ◽

pp. 1445-1461 ◽

Cited By ~ 2

Author(s):

Chaobao Huang ◽

Na An ◽

Xijun Yu ◽

Huili Zhang

Keyword(s):

Diffusion Equation ◽

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Fractional Diffusion ◽

Fractional Diffusion Equation ◽

Time Fractional Diffusion Equation

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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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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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