首页|Two-grid finite element methods for nonlinear time fractional variable coefficient diffusion equations
Two-grid finite element methods for nonlinear time fractional variable coefficient diffusion equations
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NSTL
Elsevier
? 2022 Elsevier Inc.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.
Error estimateFinite element methodL2?1σ schemeNonlinear time fractional variable coefficient diffusion equationsStabilityTwo-grid method
Zeng Y.、Tan Z.
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School of Computer Science and Engineering Sun Yat-sen University
NSTL
Elsevier
