A Fast Finite Volume Method on Locally Refined Meshes for Fractional Diffusion Equations

East Asian Journal on Applied Mathematics ◽

10.4208/eajam.271118.280319 ◽

2019 ◽

Vol 9 (4) ◽

Author(s):

Jinhong Jia ◽

Hong Wang

Keyword(s):

Finite Volume Method ◽

Finite Volume ◽

Fractional Diffusion ◽

Diffusion Equations ◽

Fractional Diffusion Equations ◽

Refined Meshes ◽

Volume Method ◽

Locally Refined Meshes

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A fast finite volume method for conservative space–time fractional diffusion equations discretized on space–time locally refined meshes

Computers & Mathematics with Applications ◽

10.1016/j.camwa.2019.04.003 ◽

2019 ◽

Vol 78 (5) ◽

pp. 1345-1356 ◽

Author(s):

Jinhong Jia ◽

Hong Wang

Keyword(s):

Finite Volume Method ◽

Finite Volume ◽

Fractional Diffusion ◽

Diffusion Equations ◽

Fractional Diffusion Equations ◽

Refined Meshes ◽

Volume Method ◽

Locally Refined Meshes

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A fast finite volume method for conservative space-fractional diffusion equations in convex domains

Journal of Computational Physics ◽

10.1016/j.jcp.2016.01.015 ◽

2016 ◽

Vol 310 ◽

pp. 63-84 ◽

Author(s):

Jinhong Jia ◽

Hong Wang

Keyword(s):

Finite Volume Method ◽

Finite Volume ◽

Fractional Diffusion ◽

Diffusion Equations ◽

Convex Domains ◽

Fractional Diffusion Equations ◽

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Analysis and efficient implementation of alternating direction implicit finite volume method for Riesz space‐fractional diffusion equations in two space dimensions

Numerical Methods for Partial Differential Equations ◽

10.1002/num.22554 ◽

2020 ◽

Vol 37 (1) ◽

pp. 818-835

Author(s):

Huan Liu ◽

Xiangcheng Zheng ◽

Hongfei Fu ◽

Hong Wang

Keyword(s):

Finite Volume Method ◽

Finite Volume ◽

Fractional Diffusion ◽

Riesz Space ◽

Diffusion Equations ◽

Alternating Direction Implicit ◽

Fractional Diffusion Equations ◽

Alternating Direction ◽

Two Space Dimensions ◽

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An efficient quadratic finite volume method for variable coefficient Riesz space‐fractional diffusion equations

Mathematical Methods in the Applied Sciences ◽

10.1002/mma.6306 ◽

2020 ◽

Author(s):

Fangli Li ◽

Hongfei Fu ◽

Jun Liu

Keyword(s):

Finite Volume Method ◽

Finite Volume ◽

Variable Coefficient ◽

Fractional Diffusion ◽

Riesz Space ◽

Diffusion Equations ◽

Fractional Diffusion Equations ◽

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An Efficient Finite Volume Method for Nonlinear Distributed-Order Space-Fractional Diffusion Equations in Three Space Dimensions

Journal of Scientific Computing ◽

10.1007/s10915-019-00979-2 ◽

2019 ◽

Vol 80 (3) ◽

pp. 1395-1418 ◽

Author(s):

Xiangcheng Zheng ◽

Huan Liu ◽

Hong Wang ◽

Hongfei Fu

Keyword(s):

Finite Volume Method ◽

Finite Volume ◽

Fractional Diffusion ◽

Diffusion Equations ◽

Fractional Diffusion Equations ◽

Volume Method ◽

Three Space ◽

Distributed Order

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A Parareal Finite Volume Method for Variable-Order Time-Fractional Diffusion Equations

Journal of Scientific Computing ◽

10.1007/s10915-020-01321-x ◽

2020 ◽

Vol 85 (1) ◽

Author(s):

Huan Liu ◽

Aijie Cheng ◽

Hong Wang

Keyword(s):

Finite Volume Method ◽

Finite Volume ◽

Fractional Diffusion ◽

Diffusion Equations ◽

Variable Order ◽

Fractional Diffusion Equations ◽

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A finite volume method for two-sided fractional diffusion equations on non-uniform meshes

Journal of Computational Physics ◽

10.1016/j.jcp.2017.01.061 ◽

2017 ◽

Vol 335 ◽

pp. 747-759 ◽

Author(s):

Alex Simmons ◽

Qianqian Yang ◽

Timothy Moroney

Keyword(s):

Finite Volume Method ◽

Finite Volume ◽

Fractional Diffusion ◽

Diffusion Equations ◽

Fractional Diffusion Equations ◽

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Stability and convergence of a Crank–Nicolson finite volume method for space fractional diffusion equations

Applied Numerical Mathematics ◽

10.1016/j.apnum.2019.01.005 ◽

2019 ◽

Vol 139 ◽

pp. 38-51 ◽

Author(s):

Hongfei Fu ◽

Yanan Sun ◽

Hong Wang ◽

Xiangcheng Zheng

Keyword(s):

Finite Volume Method ◽

Finite Volume ◽

Fractional Diffusion ◽

Diffusion Equations ◽

Stability And Convergence ◽

Fractional Diffusion Equations ◽

Volume Method ◽

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A finite volume method based on radial basis functions for two-dimensional nonlinear diffusion equations

Applied Mathematical Modelling ◽

10.1016/j.apm.2005.07.007 ◽

2006 ◽

Vol 30 (10) ◽

pp. 1118-1133 ◽

Author(s):

T.J. Moroney ◽

I.W. Turner

Keyword(s):

Finite Volume Method ◽

Radial Basis Functions ◽

Finite Volume ◽

Nonlinear Diffusion ◽

Basis Functions ◽

Diffusion Equations ◽

Two Dimensional ◽

Nonlinear Diffusion Equations ◽

Radial Basis ◽

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An upwind finite volume method for convection-diffusion equations on rectangular mesh

Chaos Solitons & Fractals ◽

10.1016/j.chaos.2018.09.011 ◽

2019 ◽

Vol 118 ◽

pp. 159-165 ◽

Author(s):

Jiawei Tan

Keyword(s):

Finite Volume Method ◽

Finite Volume ◽

Diffusion Equations ◽

Convection Diffusion ◽

Rectangular Mesh ◽

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