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W. Auzinger, O. Koch, M. Thalhammer:
"Defect based error estimation techniques for exponential splitting schemes";
Talk: 7th Austrian Numerical Analysis Day, Klagenfurt; 2011-05-05 - 2011-05-06.

Exponential splitting schemes for evolutionary problems aim for a significant reduction of the computational effort in approximating the exact evolution operator, via additive splitting of the right-hand side. Classical examples are the first order Lie-Trotter splitting and the second order Strang splitting. For these, and more general, splitting schemes, a defect can be defined by inserting the approximate splitting operator into the given evolution equation. This notion of defect leads in a natural and simple way to the well-known a priori local error bounds. Moreover, we show how a posteriori local error estimators can be constructed which only involve evaluation of the defect operator at the current approximation. We discuss rigorous bounds for the deviation of these estimators, discuss implementation issues, and present numerical results.