Space-time finite element method for the distributed-order time fractional reaction diffusion equations

Weiping Bu; Lun Ji; Yifa Tang

doi:10.1016/j.apnum.2019.11.010

journal article Jun 01, 2020

Space-time finite element method for the distributed-order time fractional reaction diffusion equations

Weiping Bu Lun Ji Yifa Tang

Applied Numerical Mathematics Vol. 152 pp. 446-465 · Elsevier BV

View at Publisher Save 10.1016/j.apnum.2019.11.010

Topics

No keywords indexed for this article. Browse by subject →

References

51

[1]

Abbaszadeh "An improved meshless method for solving two-dimensional distributed order time-fractional diffusion-wave equation with error estimate" Numer. Algorithms (2017) 10.1007/s11075-016-0201-0

[2]

Alikhanov "Numerical methods of solutions of boundary value problems for the multi-term variable-distributed order diffusion equation" Appl. Math. Comput. (2015)

[3]

Ansari "Exact solutions to some models of distributed-order time fractional diffusion equations via the Fox H functions" ScienceAsia (2013) 10.2306/scienceasia1513-1874.2013.39s.057

[4]

Atanacković (2014)

[5]

Baleanu (2012)

[6]

Bu "An h-p version of the continuous Petrov-Galerkin finite element method for Riemann-Liouville fractional differential equation with novel test basis functions" Numer. Algorithms (2019) 10.1007/s11075-018-0559-2

[7]

Finite Difference/Finite Element Methods for Distributed-Order Time Fractional Diffusion Equations

Weiping Bu, Aiguo Xiao, Wei Zeng

Journal of Scientific Computing 2017 10.1007/s10915-017-0360-8

[8]

Bu "Space-time finite element method for the multi-term time-space fractional diffusion equation on a two-dimensional domain" Comput. Math. Appl. (2018)

[9]

Chen "Finite difference/spectral approximations for the distributed order time fractional reaction-diffusion equation on an unbounded domain" J. Comput. Phys. (2016) 10.1016/j.jcp.2016.03.044

[10]

Chen "Fourth order accurate scheme for the space fractional diffusion equations" SIAM J. Numer. Anal. (2014) 10.1137/130933447

[11]

Duan "Space-time Petrov-Galerkin FEM for fractional diffusion problems" Comput. Methods Appl. Math. (2018) 10.1515/cmam-2017-0026

[12]

Fan "A numerical method for solving the two-dimensional distributed order space fractional diffusion equation on an irregular convex domain" Appl. Math. Lett. (2018) 10.1016/j.aml.2017.10.005

[13]

French "A continuous space-time finite element method for the wave equation" Math. Comput. (1996) 10.1090/s0025-5718-96-00685-0

[14]

Gao "The temporal second order difference schemes based on the interpolation approximation for solving the time multi-term and distributed-order fractional sub-diffusion equations" J. Sci. Comput. (2017) 10.1007/s10915-017-0407-x

[15]

Gorenflo "Fundamental solution of a distributed order time-fractional diffusion-wave equation as probability density" Fract. Calc. Appl. Anal. (2013) 10.2478/s13540-013-0019-6

[16]

Hilfer (2000)

[17]

Hou "Müntz spectral methods for the time-fractional diffusion equation" Comput. Methods Appl. Math. (2018) 10.1515/cmam-2017-0027

[18]

A numerical investigation of the time distributed-order diffusion model

Xiuling Hu, Fawang Liu, Vo Anh et al.

ANZIAM Journal 2013 10.21914/anziamj.v55i0.7888

[19]

Huang "Convergence analysis of a block-by-block method for fractional differential equations" Numer. Math. (2012)

[20]

Huang "Two finite difference schemes for time fractional diffusion-wave equation" Numer. Algorithms (2013) 10.1007/s11075-012-9689-0

[21]

Jiang "Fast evaluation of the Caputo fractional derivative and its applications to fractional diffusion equations" Commun. Comput. Phys. (2017) 10.4208/cicp.oa-2016-0136

[22]

Jin "Error estimates for approximations of distributed order time fractional diffusion with nonsmooth data" Fract. Calc. Appl. Anal. (2016) 10.1515/fca-2016-0005

[23]

Kilbas (2006)

[24]

Kochubei "Distributed order calculus and equations of ultraslow diffusion" J. Math. Anal. Appl. (2008) 10.1016/j.jmaa.2007.08.024

[25]

Li "High-order approximation to Caputo derivatives and Caputo-type advection-diffusion equations: revisited" Numer. Funct. Anal. Optim. (2017) 10.1080/01630563.2017.1291521

[26]

Li "High-order approximation to Caputo derivatives and Caputo-type advection-diffusion equations (III)" J. Comput. Appl. Math. (2016) 10.1016/j.cam.2015.11.037

[27]

Li "A novel finite volume method for the Riesz space distributed order advection-diffusion equation" Appl. Math. Model. (2017) 10.1016/j.apm.2017.01.065

[28]

Li "Galerkin finite element method for higher dimensional multi-term fractional diffusion equation on non-uniform meshes" Appl. Anal. (2017) 10.1080/00036811.2016.1186271

[29]

Li "Nonconforming virtual element method for the time fractional reaction-subdiffusion equation with non-smooth data" J. Sci. Comput. (2019) 10.1007/s10915-019-01064-4

[30]

Li "Two temporal second-order H1-Galerkin mixed finite element schemes for distributed-order fractional sub-diffusion equations" Numer. Algorithms (2018) 10.1007/s11075-018-0476-4

[31]

Asymptotic estimates of solutions to initial-boundary-value problems for distributed order time-fractional diffusion equations

Zhiyuan Li, Yuri Luchko, Masahiro Yamamoto

Fractional Calculus and Applied Analysis 2014 10.2478/s13540-014-0217-x

[32]

Liu "Time two-mesh algorithm combined with finite element method for time fractional water wave model" Int. J. Heat Mass Transf. (2018) 10.1016/j.ijheatmasstransfer.2017.12.118

[33]

Luchko "Boundary value problems for the generalized time-fractional diffusion equation of distributed order" Fract. Calc. Appl. Anal. (2009)

[34]

Mainardi "Some aspects of fractional diffusion equations of single and distributed order" Appl. Math. Comput. (2007)

[35]

REGULARITY OF SOLUTIONS TO A TIME-FRACTIONAL DIFFUSION EQUATION

William Mclean

The ANZIAM Journal 2010 10.1017/s1446181111000617

[36]

Meerschaert "Distributed-order fractional diffusions on bounded domains" J. Math. Anal. Appl. (2011) 10.1016/j.jmaa.2010.12.056

[37]

The random walk's guide to anomalous diffusion: a fractional dynamics approach

Ralf Metzler, Joseph Klafter

Physics Reports 2000 10.1016/s0370-1573(00)00070-3

[38]

Morgado "Numerical approximation of distributed order reaction-diffusion equations" J. Comput. Appl. Math. (2015) 10.1016/j.cam.2014.07.029

[39]

Mustapha "A discontinuous Petrov-Galerkin method for time-fractional diffusion equations" SIAM J. Numer. Anal. (2014) 10.1137/140952107

[40]

Podlubny (1998)

[41]

Ren "A numerical method for distributed order time fractional diffusion equation with weakly singular solutions" Appl. Math. Lett. (2019) 10.1016/j.aml.2019.04.030

[42]

Shen "Fast finite difference schemes for time-fractional diffusion equations with a weak singularity at initial time" East Asian J. Appl. Math. (2018) 10.4208/eajam.010418.020718

[43]

Shi "An unstructured mesh finite element method for solving the multi-term time fractional and Riesz space distributed-order wave equation on an irregular convex domain" Appl. Math. Model. (2019) 10.1016/j.apm.2019.04.023

[44]

Error Analysis of a Finite Difference Method on Graded Meshes for a Time-Fractional Diffusion Equation

Martin Stynes, Eugene O'Riordan, José Luis Gracia

SIAM Journal on Numerical Analysis 2017 10.1137/16m1082329

[45]

Sun "A new collection of real world applications of fractional calculus in science and engineering" Commun. Nonlinear Sci. Numer. Simul. (2018) 10.1016/j.cnsns.2018.04.019

[46]

Wang "An efficient fourth-order in space difference scheme for the nonlinear fractional Ginzburg-Landau equation" BIT Numer. Math. (2018) 10.1007/s10543-018-0698-9

[47]

Wei "Stability and convergence of a local discontinuous Galerkin method for the fractional diffusion equation with distributed order" J. Appl. Math. Comput. (2018)

[48]

Yang "WSGD-OSC scheme for two-dimensional distributed order fractional reaction-diffusion equation" J. Sci. Comput. (2018) 10.1007/s10915-018-0672-3

[49]

Ye "Compact difference scheme for distributed-order time-fractional diffusion-wave equation on bounded domains" J. Comput. Phys. (2015) 10.1016/j.jcp.2015.06.025

[50]

Zhang "A Crank-Nicolson ADI Galerkin-Legendre spectral method for the two-dimensional Riesz space distributed-order advection-diffusion equation" Comput. Math. Appl. (2018) 10.1016/j.camwa.2018.08.042

Showing 50 of 51 references

Metrics

32

Citations

51

References

Details

Published: Jun 01, 2020
Vol/Issue: 152
Pages: 446-465
License: View

Authors

Department of Mathematics , Universität Innsbruck, Technikerstr. 13, A-6020 Innsbruck,

Y

Yifa Tang

Academy of Mathematics and Systems Science; Chinese Academy of Sciences; University of Chinese Academy of Sciences

Funding

National Natural Science Foundation of China

Cite This Article

Weiping Bu, Lun Ji, Yifa Tang (2020). Space-time finite element method for the distributed-order time fractional reaction diffusion equations. Applied Numerical Mathematics, 152, 446-465. https://doi.org/10.1016/j.apnum.2019.11.010

Space-time finite element method for the distributed-order time fractional reaction diffusion equations

You May Also Like