Two-grid P20-P1 MFE combined with L1 scheme for nonlinear fractional diffusion equations
Yuchun Hua1, Yuelong Tang1, Zhaohui Chen2
1College of Science, Hunan University of Science and Engineering, Hunan, China
2School of Data Science, Guangzhou City University of Technology, Guangzhou, China
Keywords: two-grid method, - mixed finite element, 1 scheme, nonlinear fractional diffusion equations
Abstract
This paper presents a two-grid method for solving nonlinear time fractional diffusion equations (TFDEs). First, a fully discrete scheme is constructed by using P20- P1 mixed finite elements (MFEs) and L1 formula for spatial and temporal discretization, respectively. Second, the stability and error of the fully discrete scheme are analyzed. Third, a two-grid algorithm (TGA) based on the fully discrete scheme is proposed and its stability and error analysis results are derived. Finally, some numerical examples are provided to support the theoretical results.
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