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Two-grid finite element methods for nonlinear time fractional variable coefficient diffusion equations

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  • Zeng, Yunhua
  • Tan, Zhijun

Abstract

In this article, an efficient two-grid finite element method is proposed for solving the nonlinear time fractional variable coefficient diffusion equations. This algorithm firstly solves a nonlinear system to get the numerical solution uHn on the coarse grid with size H, then based on the initial iterative solution uHn on the coarse grid, the linearized finite element system is solved on the fine grid with size h to get the numerical solution Uhn, in which the temporal direction is approximated by the L2−1σ scheme. Besides, the stability and priori error estimates of standard finite element method and two-grid method are given. Finally, the validity and efficiency of the two-grid algorithm are verified by two numerical experiments.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:apmaco:v:434:y:2022:i:c:s0096300322004829
    DOI: 10.1016/j.amc.2022.127408
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    References listed on IDEAS

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    1. Liu, Q. & Liu, F. & Gu, Y.T. & Zhuang, P. & Chen, J. & Turner, I., 2015. "A meshless method based on Point Interpolation Method (PIM) for the space fractional diffusion equation," Applied Mathematics and Computation, Elsevier, vol. 256(C), pages 930-938.
    2. 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.
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