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W. Auzinger, O. Koch, M. Thalhammer:
"Defect-based local error estimators for splitting methods, with application to Schrödinger equations, Part I. The linear case";
in: "ASC Report 34/2011", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2011, ISBN: 978-3-902627-04-9.

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

http://www.asc.tuwien.ac.at/preprint/2011/asc34x2011.pdf