Approximating the nonlinear Schrödinger equation by a two level linearly implicit finite element method

Preprint, 2017

Abstract. We consider the study of a numerical scheme for an initial- and Dirichlet boundary- value problem for a nonlinear Schrodi nger equation. We approximate the solution using a, local (non-uniform) two l evel scheme in time (see C. Besse [6] and [7]) combined with, an optimal, finite el ement strategy for the discretization in the spatial variable based on stud ies outlined as, e.g. in [2] and [10]. For the proposed fully discrete scheme, we show convergence both in L2 and H1 norms.