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A posteriori error analysis for the Crank-Nicolson method for linear Schrödinger equations*
Published online by Cambridge University Press: 21 February 2011
Abstract
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.
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- Type
- Research Article
- Information
- ESAIM: Mathematical Modelling and Numerical Analysis , Volume 45 , Issue 4 , July 2011 , pp. 761 - 778
- Copyright
- © EDP Sciences, SMAI, 2011
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