Abstract
Abstract An error estimate is presented for the Newton iterative Crank–Nicolson finite element method for the nonlinear Schrödinger equation, fully discretized by quadrature, without restriction on the grid ratio between temporal step size and spatial mesh size. It is shown that the Newton iterative solution converges double exponentially with respect to the number of iterations to the solution of the implicit Crank–Nicolson method uniformly for all time levels, with optimal convergence in both space and time.
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