On the convergence of a linear two-step finite element method for the nonlinear Schrödinger equation
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 35 (2001) no. 3, p. 389-405

We discretize the nonlinear Schrödinger equation, with Dirichlet boundary conditions, by a linearly implicit two-step finite element method which conserves the ${L}^{2}$ norm. We prove optimal order a priori error estimates in the ${L}^{2}$ and ${H}^{1}$ norms, under mild mesh conditions for two and three space dimensions.

Classification:  65M12,  65M60
Keywords: nonlinear Schrödinger equation, two-step time discretization, linearly implicit method, finite element method, ${L}^{2}$ and ${H}^{1}$ error estimates, optimal order of convergence
@article{M2AN_2001__35_3_389_0,
author = {Zouraris, Georgios E.},
title = {On the convergence of a linear two-step finite element method for the nonlinear Schr\"odinger equation},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
publisher = {EDP-Sciences},
volume = {35},
number = {3},
year = {2001},
pages = {389-405},
zbl = {0991.65088},
mrnumber = {1837077},
language = {en},
url = {http://www.numdam.org/item/M2AN_2001__35_3_389_0}
}

Zouraris, Georgios E. On the convergence of a linear two-step finite element method for the nonlinear Schrödinger equation. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 35 (2001) no. 3, pp. 389-405. http://www.numdam.org/item/M2AN_2001__35_3_389_0/

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