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

Qingfeng Li, Yanping Chen, Yunqing Huang and Yang Wang

Mathematics and Computers in Simulation (MATCOM), 2021, vol. 185, issue C, 436-451

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.

Keywords: Two-grid method; Finite element method; L1 scheme; Nonlinear time fractional diffusion equations (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:185:y:2021:i:c:p:436-451

DOI: 10.1016/j.matcom.2020.12.033

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