Defect-based local error estimators for splitting methods, with application to Schrödinger equations, Part I: The linear case

Authors:
Winfried Auzinger;Othmar Koch;Mechthild Thalhammer
Affiliations:
Institute for Analysis and Scientific Computing, Vienna University of Technology, Wiedner Hauptstraíe 8-10, A-1040 Wien, Austria;Institute for Analysis and Scientific Computing, Vienna University of Technology, Wiedner Hauptstraíe 8-10, A-1040 Wien, Austria;Institut für Mathematik, Leopold-Franzens Universität Innsbruck, Technikerstraíe13/VII, A-6020 Innsbruck, Austria and Institut für Mathematik und Rechneranwendung, Fakultä ...
Venue:
Journal of Computational and Applied Mathematics
Year:
2012

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Abstract

We introduce a defect correction principle for exponential operator splitting methods applied to time-dependent linear Schrodinger equations and construct a posteriori local error estimators for the Lie-Trotter and Strang splitting methods. Under natural commutator bounds on the involved operators we prove asymptotical correctness of the local error estimators, and along the way recover the known a priori convergence bounds. Numerical examples illustrate the theoretical local and global error estimates.