Defect-based local error estimators for high-order splitting methods involving three linear operators
Prior work on high-order exponential operator splitting methods is extended to evolution equations defined 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 confirm the asymptotical correctness of the proposed a posteriori error estimators.
http://phaidra.univie.ac.at/o:423891
Wissenschaftlicher Artikel
Angenommene Version
06.11.2014
70
1
61-91
Springer
Englisch
Frei zugänglich
07.11.2015
P24157-N13 – Fonds zur Förderung der wissenschaftlichen Forschung (FWF)
1017-1398
Linear evolution equations; Time integration methods; High-order exponential operator splitting methods; Local error; A posteriori local error estimators
Dewey Dezimal Klassifikation → Naturwissenschaften und Mathematik → Mathematik → Numerical analysis