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A posteriori error analysis for the Crank-Nicolson method for linear Schrödinger equations

Irene Kyza — 2011

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We prove error estimates of optimal order for linear Schrödinger-type equations in the ( )- and the ( )-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 in [ 75 (2006) 511–531], leads to upper bounds that are of optimal order in the ( )-norm, but of suboptimal order in the ( ...

error analysis for the Crank-Nicolson method for linear Schrödinger equations

Irene Kyza — 2011

ESAIM: Mathematical Modelling and Numerical Analysis

We prove error estimates of optimal order for linear Schrödinger-type equations in the ( )- and the ( )-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 in [ (2006) 511–531], leads to upper bounds that are of optimal order in the ( )-norm, but of suboptimal order in the ( ...

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