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W. Auzinger, O. Koch, M. Thalhammer:
"Defect-based local error estimators for high-order splitting methods involving three linear operators";
Numerical Algorithms, 70 (2015), 1; S. 61 - 91.

Prior work on high-order exponential operator splitting methods is extended to evolution equations de ned by three linear operators. A posteriori local error estimators are constructed via a suitable integral representation of the local error involving the defect associated with the splitting solution and quadrature approximation via Hermite interpolation. In order to prove asymptotical correctness, a multiple integral representation involving iterated defects is deduced by repeated application of the variation-of-constant formula. The error analysis within the framework of abstract evolution equations provides the basis for concrete applications. Numerical examples for initial-boundary value problems of Schrödinger and of parabolic type con rm the asymptotical correctness of the proposed a posteriori error estimators.

Linear evolution equations, time integration methods, high-order exponential operator splitting methods

http://dx.doi.org/10.1007/s11075-014-9935-8

http://link.springer.com/article/10.1007/s11075-014-9935-8

Projektleitung Othmar Koch:
Adaptives Splitting für nichtlineare Schrödingergleichungen