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W. Auzinger, O. Koch, M. Thalhammer:
"Local error estimation for exponential splitting schemes";
Vortrag: Conference on Simulation and Optimization, Györ (eingeladen); 29.06.2011 - 01.07.2011.

Exponential splitting schemes for evolutionary problems aim for a significant reduction of the computational effort via additive splitting of the right-hand side. Classical examples are the first order Lie-Trotter splitting and the second order Strang splitting. For the purpose of local error estimation with the aim of stepsize control, we use a defect-based approach. The idea is to consider the defect of the splitting approximation, defined by inserting its flow into the original evolution equation. Moreover, the splitting flow exactly satisfies a modified evolution equation. Solving this modified problem, with defect added, leads in a natural way to a local posteriori error estimate, which can be computationally realized with sufficient accuracy by means of appropriate quadrature. This in turn amounts to evaluation of the action of the defect on the current approximation, involving some moderate additional effort in each integration step. In this talk we concentrate on linear problems; bounds for the deviation of the estimator as well as implementation issues are discussed, and preliminary numerical results are presented.

exponential splitting schemes, defect correction, error estimation