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Non-uniform L1/discontinuous Galerkin approximation for the time-fractional convection equation with weak regular solution

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  • Li, Changpin
  • Wang, Zhen

Abstract

In this paper, an efficient method seeking the numerical solution of a time-fractional convection equation whose solution is not smooth at the starting time is presented. The Caputo time-fractional derivative of order in (0,1) is discretized by the L1 finite difference method using non-uniform meshes; and, for the spatial derivative the discontinuous Galerkin (DG) finite element method is used. The stability and convergence of the method are analyzed for two-dimensional domains, using Cartesian and a particular class of unstructured grids. At last, several numerical examples are carried out which support the theoretical analysis.

Suggested Citation

  • Li, Changpin & Wang, Zhen, 2021. "Non-uniform L1/discontinuous Galerkin approximation for the time-fractional convection equation with weak regular solution," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 182(C), pages 838-857.
    • Handle: RePEc:eee:matcom:v:182:y:2021:i:c:p:838-857
    DOI: 10.1016/j.matcom.2020.12.007
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    References listed on IDEAS

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    1. Li, Changpin & Wang, Zhen, 2020. "The discontinuous Galerkin finite element method for Caputo-type nonlinear conservation law," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 169(C), pages 51-73.
    2. Shen, Jinye & Sun, Zhi-zhong & Cao, Wanrong, 2019. "A finite difference scheme on graded meshes for time-fractional nonlinear Korteweg-de Vries equation," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 752-765.
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    Citations

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    Cited by:

    1. Wei, Leilei & Li, Wenbo, 2021. "Local discontinuous Galerkin approximations to variable-order time-fractional diffusion model based on the Caputo–Fabrizio fractional derivative," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 188(C), pages 280-290.
    2. Li, Lili & Zhao, Dan & She, Mianfu & Chen, Xiaoli, 2022. "On high order numerical schemes for fractional differential equations by block-by-block approach," Applied Mathematics and Computation, Elsevier, vol. 425(C).
    3. Li, Changpin & Li, Dongxia & Wang, Zhen, 2021. "L1/LDG method for the generalized time-fractional Burgers equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 187(C), pages 357-378.

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    More about this item

    Keywords

    Time-fractional convection equation; L1 scheme; Discontinuous Galerkin method; Rectangular element; Triangular element;
    All these keywords.

    JEL classification:

    • L1 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance

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