Superconvergence of Finite Element Approximations of the Two-Dimensional Cubic Nonlinear Schrodinger Equation

The superconvergence of a two-dimensional time-independent nonlinear Schrodinger equation are analyzed with the rectangular Lagrange typefinite element of order k.Firstly,the error estimate and superclose property are given in H^(1)-norm with order O(h^(k+1))between thefinite element solution u_(h) and the interpolation func-tion uI 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.