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

Yunhua Zeng and Zhijun Tan

Applied Mathematics and Computation, 2022, vol. 434, issue C

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.

Keywords: Nonlinear time fractional variable coefficient diffusion equations; Two-grid method; Finite element method; L2−1σ scheme; Stability; Error estimate (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:434:y:2022:i:c:s0096300322004829

DOI: 10.1016/j.amc.2022.127408

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