Publications in Scientific Journals:
W. Auzinger, O. Koch, M. Thalhammer:
"Defect-based local error estimators for splitting methods, with application to Schrödinger equations, Part I. The linear case";
Journal of Computational and Applied Mathematics,
236
(2012),
ISBN: 978-3-902627-04-9;
2643
- 2659.
English abstract:
We introduce a defect correction principle for exponential operator splitting methods
applied to time-dependent linear Schrödinger equations and
construct a posteriori local error estimators for the Lie-Trotter and Strang splitting methods.
Under natural commutator bounds on the involved operators we prove asymptotical correctness of
the local error estimators, and along the way recover the known a priori convergence bounds.
Numerical examples illustrate the theoretical local and global error estimates
Keywords:
Linear evolution equations, Time-dependent linear Schrödinger equations, Time integration, Exponential operator splitting methods, Defect correction, A priori local error estimates, A posteriori local error estimates
"Official" electronic version of the publication (accessed through its Digital Object Identifier - DOI)
http://dx.doi.org/10.1016/j.cam.2012.01.001
Electronic version of the publication:
http://www.sciencedirect.com/science/article/pii/S0377042712000027
Related Projects:
Project Head Othmar Koch:
Adaptives Splitting für nichtlineare Schrödingergleichungen
Created from the Publication Database of the Vienna University of Technology.