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Title: A discrete variational principle for rate-independent evolution
Authors: Mielke, AlexanderStefanelli, Ulisse
Issue Date: 2008
Published in: Preprint / Weierstraß-Institut für Angewandte Analysis und Stochastik , Volume 1295, 0946-8633
Publisher: Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik
Abstract: We develop a global-in-time variational approach to the time-discretization of rate-independent processes. In particular, we investigate a discrete version of the variational principle based on the weighted energy-dissipation functional introduced by A. Mielke and M. Ortiz in ESAIM Control Optim. Calc. Var., 2008. We prove the conditional convergence of time-discrete approximate minimizers to energetic solutions of the time-continuous problem. Moreover, the convergence result is combined with approximation and relaxation. For a fixed partition the functional is shown to have an asymptotic development by Gamma convergence, cf. G. Anzellotti and S. Baldo (Appl. Math. Optim., 1993), in the limit of vanishing viscosity.
Keywords: Variational Principle; rate-independent process; time-discretization
DDC: 510
License: This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.
Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.
Appears in Collections:Mathematik



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