Two-Grid Method for a Fully Discrete Mixed Finite Element Solution of the Time-Dependent Schrodinger Equation

We study the backward Euler fully discrete mixed finite element method for the time-dependent Schrodinger equation; the error result of the mixed finite element solution is obtained in the L-2-norm with order O(t+h(k+1)). Then, a two-grid method is presented with a backward Euler fully discrete scheme. Using this method, we solve the original problem on a much coarser grid and solve elliptic equations on a fine grid. In addition, the error of the two-grid solution is also obtained in the L-2-norm with order O(t+h(k+1)+Hk+2). The numerical experiment is provided to demonstrate the efficiency of the algorithm.