A note on optimal H^1-error estimates for Crank-Nicolson approximations to the nonlinear Schrödinger equation

07/05/2019

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by   Patrick Henning, et al.

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In this paper we consider a mass- and energy--conserving Crank-Nicolson time discretization for a general class of nonlinear Schrödinger equations. This scheme, which enjoys popularity in the physics community due to its conservation properties, was already subject to several analytical and numerical studies. However, a proof of optimal L^∞(H^1)-error estimates is still open, both in the semi-discrete Hilbert space setting, as well as in fully-discrete finite element settings. This paper aims at closing this gap in the literature.