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Two-grid methods for nonlinear time fractional diffusion equations by L1-Galerkin FEM

Author

Listed:
  • Li, Qingfeng
  • Chen, Yanping
  • Huang, Yunqing
  • Wang, Yang

Abstract

In this paper, two efficient two-grid algorithms with L1 scheme are presented for solving two-dimensional nonlinear time fractional diffusion equations. The classical L1 scheme is considered in the time direction, and the two-grid FE method is used to approximate spatial direction. To linearize the discrete equations, the Newton iteration approach and correction technique are applied. The two-grid algorithms reduce the solution of the nonlinear fractional problem on a fine grid to one linear equation on the same fine grid and an original nonlinear problem on a much coarser grid. As a result, our algorithms save total computational cost. Theoretical analysis shows that the two-grid algorithms maintain asymptotically optimal accuracy. Moreover, the numerical experiment presented further confirms the theoretical results.

Suggested Citation

  • Li, Qingfeng & Chen, Yanping & Huang, Yunqing & Wang, Yang, 2021. "Two-grid methods for nonlinear time fractional diffusion equations by L1-Galerkin FEM," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 185(C), pages 436-451.
    • Handle: RePEc:eee:matcom:v:185:y:2021:i:c:p:436-451
    DOI: 10.1016/j.matcom.2020.12.033
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    References listed on IDEAS

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    1. Wang, Yang & Chen, Yanping & Huang, Yunqing, 2020. "A two-grid method for semi-linear elliptic interface problems by partially penalized immersed finite element methods," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 169(C), pages 1-15.
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    Cited by:

    1. Zeng, Yunhua & Tan, Zhijun, 2022. "Two-grid finite element methods for nonlinear time fractional variable coefficient diffusion equations," Applied Mathematics and Computation, Elsevier, vol. 434(C).

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    More about this item

    Keywords

    Two-grid method; Finite element method; L1 scheme; Nonlinear time fractional diffusion equations;
    All these keywords.

    JEL classification:

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

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