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

ESAIM: Mathematical Modelling and Numerical Analysis (2011)

- 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 45.4 (2011): 761-778. <http://eudml.org/doc/197399>.

@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},

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

language = {eng},

month = {2},

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/197399},

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

DA - 2011/2//

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; linear Schrödinger equation; Crank-Nicolson reconstruction; a posteriori error analysis; energy techniques; - and -norm; numerical examples

UR - http://eudml.org/doc/197399

ER -

## References

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