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A Weak Galerkin Finite Element Method for High Dimensional Time-fractional Diffusion Equation

Author

Listed:
  • Wang, Xiuping
  • Gao, Fuzheng
  • Liu, Yang
  • Sun, Zhengjia

Abstract

This paper is concerned with the application of a weak Galerkin finite element method (WG-FEM) to the time-fractional diffusion equation. The WG-FEM with L1-formula and the fast evaluation scheme based on WG-FEM are designed. The optimal convergence rates for both semi-discrete and fully discrete WG-FEM schemes are obtained, and the stability analysis for the semi-discrete WG-FEM is derived. Numerical experiments are implemented to verify the theoretical results.

Suggested Citation

  • Wang, Xiuping & Gao, Fuzheng & Liu, Yang & Sun, Zhengjia, 2020. "A Weak Galerkin Finite Element Method for High Dimensional Time-fractional Diffusion Equation," Applied Mathematics and Computation, Elsevier, vol. 386(C).
    • Handle: RePEc:eee:apmaco:v:386:y:2020:i:c:s0096300320304823
    DOI: 10.1016/j.amc.2020.125524
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    References listed on IDEAS

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    1. 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).
    2. Qin, Hongyu & Zhang, Qifeng & Wan, Shaohua, 2019. "The continuous Galerkin finite element methods for linear neutral delay differential equations," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 76-85.
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    Cited by:

    1. Hafez, Ramy M. & Zaky, Mahmoud A. & Hendy, Ahmed S., 2021. "A novel spectral Galerkin/Petrov–Galerkin algorithm for the multi-dimensional space–time fractional advection–diffusion–reaction equations with nonsmooth solutions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 678-690.
    2. Sun, Lu-Yao & Fang, Zhi-Wei & Lei, Siu-Long & Sun, Hai-Wei & Zhang, Jia-Li, 2022. "A fast algorithm for two-dimensional distributed-order time-space fractional diffusion equations," Applied Mathematics and Computation, Elsevier, vol. 425(C).

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