Superconvergence analysis of a two-grid finite element method for nonlinear time-fractional diffusion equations

Based on spatial finite-element methods combined with classical L1 time stepping method, the superconvergence analysis of the two-grid approximate scheme for the two-dimensional nonlinear time-fractional diffusion equations is considered. First, we use the rectangular Lagrange type finite element of order p to get a two-grid fully discrete scheme of the equation and discuss the superclose error estimate with the order O (h(p+1) + H2p+2 + tau(2-alpha)) in the H-1 norm, here tau, H and h denote time step, coarse and fine grid sizes, respectively. Second, through the interpolated postprocessing approach, the global superconvergence of order O (h(2) + H-4 + tau(2-alpha)) in the H-1 norm is obtained. Finally, two numerical experiments are provided to confirm our theoretical results and effectiveness of the proposed algorithm.