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Titel
A-priori error analysis of local incremental minimization schemes for rate-independent evolutions / C. Meyer, M. Sievers
VerfasserMeyer, Christian ; Sievers, Michael
ErschienenDortmund : Technische Universität Dortmund, Fakultät für Mathematik, July 2019
Ausgabe
Elektronische Ressource
Umfang1 Online-Ressource (27 Seiten) : Illustrationen
SerieErgebnisberichte angewandte Mathematik ; no. 610
SchlagwörterA-priori-Abschätzung / Numerische Mathematik
URNurn:nbn:de:hbz:6:2-115466 
DOI10.17877/DE290R-20120 
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A-priori error analysis of local incremental minimization schemes for rate-independent evolutions [0.68 mb]
Zusammenfassung

This paper is concerned with a priori error estimates for the local incremental minimization scheme, which is an implicit time discretization method for the approximation of rate-independent systems with non-convex energies. We first show by means of a counterexample that one cannot expect global convergence of the scheme without any further assumptions on the energy. For the class of uniformly convex energies, we derive error estimates of optimal order, provided that the Lipschitz constant of the load is sufficiently small. Afterwards, we extend this result to the case of an energy, which is only locally uniformly convex in a neighborhood of a given solution trajectory. For the latter case, the local incremental minimization scheme turns out to be superior compared to its global counterpart, as a numerical example demonstrates.

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