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A Crank–Nicolson Finite Volume Element Method for Time Fractional Sobolev Equations on Triangular Grids

Author

Listed:
  • Jie Zhao

    (School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China
    School of Statistics and Mathematics, Inner Mongolia University of Finance and Economics, Hohhot 010070, China)

  • Zhichao Fang

    (School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China)

  • Hong Li

    (School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China)

  • Yang Liu

    (School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China)

Abstract

In this paper, a finite volume element (FVE) method is proposed for the time fractional Sobolev equations with the Caputo time fractional derivative. Based on the L 1 -formula and the Crank–Nicolson scheme, a fully discrete Crank–Nicolson FVE scheme is established by using an interpolation operator I h * . The unconditional stability result and the optimal a priori error estimate in the L 2 ( Ω ) -norm for the Crank–Nicolson FVE scheme are obtained by using the direct recursive method. Finally, some numerical results are given to verify the time and space convergence accuracy, and to examine the feasibility and effectiveness for the proposed scheme.

Suggested Citation

  • Jie Zhao & Zhichao Fang & Hong Li & Yang Liu, 2020. "A Crank–Nicolson Finite Volume Element Method for Time Fractional Sobolev Equations on Triangular Grids," Mathematics, MDPI, vol. 8(9), pages 1-17, September.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:9:p:1591-:d:414098
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    References listed on IDEAS

    as
    1. Sayevand, K. & Arjang, F., 2016. "Finite volume element method and its stability analysis for analyzing the behavior of sub-diffusion problems," Applied Mathematics and Computation, Elsevier, vol. 290(C), pages 224-239.
    2. Yin, Baoli & Liu, Yang & Li, Hong, 2020. "A class of shifted high-order numerical methods for the fractional mobile/immobile transport equations," Applied Mathematics and Computation, Elsevier, vol. 368(C).
    3. Jie Zhao & Hong Li & Zhichao Fang & Yang Liu, 2019. "A Mixed Finite Volume Element Method for Time-Fractional Reaction-Diffusion Equations on Triangular Grids," Mathematics, MDPI, vol. 7(7), pages 1-18, July.
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