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

Zhaojie Zhou; Chenyang Zhang

doi:10.1007/s11075-017-0445-3

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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Legendre pseudo-spectral method for optimal control problem governed by a time-fractional diffusion equation

International Journal of Computer Mathematics ◽

10.1080/00207160.2017.1417591 ◽

2018 ◽

Vol 95 (6-7) ◽

pp. 1308-1325 ◽

Cited By ~ 5

Author(s):

Shengyue Li ◽

Zhaojie Zhou

Keyword(s):

Optimal Control ◽

Optimal Control Problem ◽

Diffusion Equation ◽

Control Problem ◽

Spectral Method ◽

Fractional Diffusion ◽

Fractional Diffusion Equation ◽

Time Fractional Diffusion Equation ◽

Pseudo Spectral Method ◽

Pseudo Spectral

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Error estimate for indirect spectral approximation of optimal control problem governed by fractional diffusion equation with variable diffusivity coefficient

Applied Numerical Mathematics ◽

10.1016/j.apnum.2021.07.021 ◽

2021 ◽

Author(s):

Fangyuan Wang ◽

Xiangcheng Zheng ◽

Zhaojie Zhou

Keyword(s):

Optimal Control ◽

Optimal Control Problem ◽

Diffusion Equation ◽

Error Estimate ◽

Control Problem ◽

Fractional Diffusion ◽

Fractional Diffusion Equation ◽

Diffusivity Coefficient ◽

Spectral Approximation ◽

Variable Diffusivity

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On spectral Petrov-Galerkin method for solving optimal control problem governed by a two-sided fractional diffusion equation

Computers & Mathematics with Applications ◽

10.1016/j.camwa.2021.12.020 ◽

2022 ◽

Vol 107 ◽

pp. 104-116

Author(s):

Shengyue Li ◽

Wanrong Cao ◽

Yibo Wang

Keyword(s):

Optimal Control ◽

Optimal Control Problem ◽

Diffusion Equation ◽

Control Problem ◽

Galerkin Method ◽

Fractional Diffusion ◽

Fractional Diffusion Equation

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Fractional spectral collocation method for optimal control problem governed by space fractional diffusion equation

Applied Mathematics and Computation ◽

10.1016/j.amc.2019.01.018 ◽

2019 ◽

Vol 350 ◽

pp. 331-347

Author(s):

Shengyue Li ◽

Zhaojie Zhou

Keyword(s):

Optimal Control ◽

Optimal Control Problem ◽

Diffusion Equation ◽

Control Problem ◽

Collocation Method ◽

Fractional Diffusion ◽

Fractional Diffusion Equation ◽

Spectral Collocation Method ◽

Spectral Collocation ◽

Space Fractional Diffusion Equation

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Finite element approximation of optimal control problems governed by time fractional diffusion equation

Computers & Mathematics with Applications ◽

10.1016/j.camwa.2015.11.014 ◽

2016 ◽

Vol 71 (1) ◽

pp. 301-318 ◽

Cited By ~ 24

Author(s):

Zhaojie Zhou ◽

Wei Gong

Keyword(s):

Optimal Control ◽

Finite Element ◽

Diffusion Equation ◽

Optimal Control Problems ◽

Finite Element Approximation ◽

Fractional Diffusion ◽

Fractional Diffusion Equation ◽

Control Problems ◽

Element Approximation ◽

Time Fractional Diffusion Equation

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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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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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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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