A posteriori error analysis for the Crank-Nicolson method for linear Schrödinger equations
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 45 (2011) no. 4, p. 761-778

We prove a posteriori error estimates of optimal order for linear Schrödinger-type equations in the L∞(L2)- and the L∞(H1)-norm. We discretize only in time by the Crank-Nicolson method. The direct use of the reconstruction technique, as it has been proposed by Akrivis et al. in [Math. Comput. 75 (2006) 511-531], leads to a posteriori upper bounds that are of optimal order in the L∞(L2)-norm, but of suboptimal order in the L∞(H1)-norm. The optimality in the case of L∞(H1)-norm is recovered by using an auxiliary initial- and boundary-value problem.

DOI : https://doi.org/10.1051/m2an/2010101
Classification:  65M15,  35Q41
Keywords: linear Schrödinger equation, Crank-Nicolson method, crank-nicolson reconstruction, a posteriori error analysis, energy techniques, L∞(L2)- and L∞(H1)-norm
@article{M2AN_2011__45_4_761_0,
author = {Kyza, Irene},
title = {A posteriori error analysis for the Crank-Nicolson method for linear Schr\"odinger equations},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
publisher = {EDP-Sciences},
volume = {45},
number = {4},
year = {2011},
pages = {761-778},
doi = {10.1051/m2an/2010101},
zbl = {1269.65088},
language = {en},
url = {http://www.numdam.org/item/M2AN_2011__45_4_761_0}
}

Kyza, Irene. A posteriori error analysis for the Crank-Nicolson method for linear Schrödinger equations. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 45 (2011) no. 4, pp. 761-778. doi : 10.1051/m2an/2010101. http://www.numdam.org/item/M2AN_2011__45_4_761_0/

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