A-priori error analysis of local incremental minimization schemes for rate-independent evolutions

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dc.contributor.authorMeyer, Christian
dc.contributor.authorSievers, Michael
dc.date.accessioned2019-07-12T10:47:48Z
dc.date.available2019-07-12T10:47:48Z
dc.date.issued2019-07
dc.description.abstractThis 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.de
dc.identifier.issn2190-1767
dc.identifier.urihttp://hdl.handle.net/2003/38139
dc.identifier.urihttp://dx.doi.org/10.17877/DE290R-20120
dc.language.isoen
dc.relation.ispartofseriesErgebnisberichte des Instituts für Angewandte Mathematik;610
dc.subjectrate independent evolutionsen
dc.subjectincremental minimization schemesen
dc.subjecta priori error analysisen
dc.subjectimplicit time discretizationen
dc.subjectparameterized solutionsen
dc.subjectdifferential solutionsen
dc.subject.ddc610
dc.titleA-priori error analysis of local incremental minimization schemes for rate-independent evolutionsen
dc.typeText
dc.type.publicationtypepreprint
dcterms.accessRightsopen access
eldorado.secondarypublicationfalse

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