Titel
Defect-based local error estimators for high-order splitting methods involving three linear operators
Autor*in
Winfried Auzinger
Technische Universität Wien
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Abstract
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.
Stichwort
Linear evolution equationsTime integration methodsHigh-order exponential operator splitting methodsLocal errorA posteriori local error estimators
Objekt-Typ
Sprache
Englisch [eng]
Persistent identifier
Erschienen in
Titel
Numerical Algorithms
Band
70
Ausgabe
1
Seitenanfang
61
Seitenende
91
Publication
Springer
Version
Verfügbarkeitsdatum
07.11.2015
Datum der Annahme zur Veröffentlichung
06.11.2014
Zugänglichkeit
Rechte
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