Two-grid $P_0^2-P_1$ MFE combined with $L1$ scheme for nonlinear fractional diffusion equations

This paper presents a two-grid method for solving nonlinear time fractional diffusion equations (TFDEs). First, a fully discrete scheme is constructed by using $P_0^2-P_1$ 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.