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The discontinuous Galerkin finite element method for Caputo-type nonlinear conservation law

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  • Li, Changpin
  • Wang, Zhen

Abstract

In this paper, efficient methods for numerical solutions of Caputo-type nonlinear conservation laws are established and studied, where the time fractional derivative with order in (0,1) is discretized by the finite difference method and the spatial derivative by the discontinuous Galerkin finite element method. The derived numerical schemes for one and two space dimensions are shown to be stable and convergent. Numerical experiments are provided to support these conclusions.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:169:y:2020:i:c:p:51-73
    DOI: 10.1016/j.matcom.2019.09.021
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    Cited by:

    1. Gao, Xinghua & Yin, Baoli & Li, Hong & Liu, Yang, 2021. "TT-M FE method for a 2D nonlinear time distributed-order and space fractional diffusion equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 181(C), pages 117-137.
    2. Yonggang Chen & Yu Qiao & Xiangtuan Xiong, 2022. "Regularization Error Analysis for a Sideways Problem of the 2D Nonhomogeneous Time-Fractional Diffusion Equation," Mathematics, MDPI, vol. 10(10), pages 1-14, May.
    3. 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.
    4. 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.
    5. Wei, Leilei & Wang, Huanhuan, 2023. "Local discontinuous Galerkin method for multi-term variable-order time fractional diffusion equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 203(C), pages 685-698.

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