(untitled) (Journal of Computational Mathematics, 2024)
A two-grid finite element method with L1 scheme is presented for solving two-dimensional time-fractional nonlinear Schrödinger equation. The finite element solution in the L^∞-norm are proved bounded without any time-step size conditions (dependent on spatial-step size). The classical L1 scheme is considered in the time direction, and the two-grid finite element method is applied in spatial direction. The optimal order error estimations of the two-grid solution in the L^p-norm is proved without any time-step size conditions. It is shown, both theoretically and numerically, that the coarse space can be extremely coarse, with no loss in the order of accuracy.