(untitled) (Advances in Applied Mathematics and Mechanics, 2018)
In this paper, we investigate the superconvergence property of a time-dependent nonlinear Schrödinger equation with the bilinear finite element method on the rectangular mesh. We prove the superclose error estimate in H^1-norm with order O(h^2) between the approximated solution and the elliptic projection of the exact solution. Moreover, we obtain the global superconvergence result in H^1-norm with order O(h^2) by the interpolation post-processing operator.