A two-grid discretization method for nonlinear Schrodinger equation by mixed finite element methods

In this paper, we investigate a two-grid discretization method for the two-dimensional time-dependent nonlinear Schrodinger equation by mixed finite element methods. Firstly, we solve original nonlinear Schrodinger equation on a much coarser grid. Then, we solve linear Schrodinger equation on the fine grid. We also propose the error estimate of the two-grid solution with the exact solution in L-2-norm with order O(h(k+1) + H2k+2). It is shown that our two-grid algorithm can achieve asymptotically optimal approximations as long as the mesh sizes satisfy h = O(H-2). Finally, two numerical experiments in the RT0 space are provided to partly verify the accuracy and efficiency of the two-grid algorithm.