Two-grid finite element methods for nonlinear time fractional variable coefficient diffusion equations
作者：
Highlights：
• We establish an efficient two-grid finite element algorithm for the nonlinear time fractional variable coefficient diffusion equations. The stability and convergence results are given in both two-grid scheme and fully discrete scheme.
• We consider the temporal discretization of a high-order L2−1σ scheme, which can achieved second-order numerical accuracy.
• We use two-grid finite element methods to approximate spatial direction. The optimal convergence order in the H1(Ω) can be derived when the coarse-grid of size H and the fine-grid of size h satisfyH=O(h14).
• Due to nonlinear terms, the nonlinear equation must be solved iteratively in calculations. Two-grid finite element methods can reduce the storage, save a large amount of time and maintain the numerical precision.
摘要
•We establish an efficient two-grid finite element algorithm for the nonlinear time fractional variable coefficient diffusion equations. The stability and convergence results are given in both two-grid scheme and fully discrete scheme.•We consider the temporal discretization of a high-order L2−1σ scheme, which can achieved second-order numerical accuracy.•We use two-grid finite element methods to approximate spatial direction. The optimal convergence order in the H1(Ω) can be derived when the coarse-grid of size H and the fine-grid of size h satisfyH=O(h14).•Due to nonlinear terms, the nonlinear equation must be solved iteratively in calculations. Two-grid finite element methods can reduce the storage, save a large amount of time and maintain the numerical precision.
论文关键词：Nonlinear time fractional variable coefficient diffusion equations,Two-grid method,Finite element method,L2−1σ scheme,Stability,Error estimate
论文评审过程：Received 16 April 2022, Revised 1 July 2022, Accepted 12 July 2022, Available online 29 July 2022, Version of Record 29 July 2022.
论文官网地址：https://doi.org/10.1016/j.amc.2022.127408
