(untitled) (Advances in Applied Mathematics and Mechanics, 2022)
The superconvergence of a two-dimensional time-independent nonlinear Schrödinger equation are analyzed with the rectangular Lagrange type finite element of order k. Firstly, the error estimate and superclose property are given in H^1-norm with order O(h^k+1) between the finite element solution u_h and the interpolation function u_I by use of the elliptic projection operator. Then, the global superconvergence is obtained by the interpolation post-processing technique. In addition, some numerical examples with the order k = 1 and k = 2 are provided to demonstrate the theoretical analysis.