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

- Volume: 45, Issue: 4, page 761-778
- ISSN: 0764-583X

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topKyza, 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 45.4 (2011): 761-778. <http://eudml.org/doc/273327>.

@article{Kyza2011,

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.},

author = {Kyza, Irene},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},

keywords = {linear Schrödinger equation; Crank-Nicolson method; crank-nicolson reconstruction; a posteriori error analysis; energy techniques; L∞(L2)- and L∞(H1)-norm; Crank-Nicolson reconstruction; - and -norm; numerical examples},

language = {eng},

number = {4},

pages = {761-778},

publisher = {EDP-Sciences},

title = {A posteriori error analysis for the Crank-Nicolson method for linear Schrödinger equations},

url = {http://eudml.org/doc/273327},

volume = {45},

year = {2011},

}

TY - JOUR

AU - Kyza, Irene

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

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

PY - 2011

PB - EDP-Sciences

VL - 45

IS - 4

SP - 761

EP - 778

AB - 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.

LA - eng

KW - linear Schrödinger equation; Crank-Nicolson method; crank-nicolson reconstruction; a posteriori error analysis; energy techniques; L∞(L2)- and L∞(H1)-norm; Crank-Nicolson reconstruction; - and -norm; numerical examples

UR - http://eudml.org/doc/273327

ER -

## References

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