Superconvergence analysis of a linearized energy-conservative Galerkin method for the nonlinear Schriidinger equation with wave operator

In this paper, based on a modified leap-frog scheme used in temporal direction and bilinear rectangular element applied in spatial direction, the superconvergence of Galerkin approximation are investigated for the cubic nonlinear Schrodinger equation with wave operator. The key issue to our analysis is to obtain the boundedness of the numerical solution in H-1- norm, which is indeed different from the boundedness of the L-infinity- norm required in the previous literatures. The unconditionally superconvergence error estimates are obtained without any restrictions between time stepsize and spatial meshsize. Finally, some numerical results are provided to support the theoretical analysis.