[Back]

W. Auzinger, O. Koch, M. Thalhammer:
"Defect-based local error estimators for high-order splitting methods involving three linear operators";
in: "ASC Report 22/2014", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2014, ISBN: 978-3-902627-07-0, 1 - 26.

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://www.asc.tuwien.ac.at/preprint/2014/asc22x2014.pdf